diff --git a/mdformat/_cli.py b/mdformat/_cli.py
index db9a8dcc..89b63b40 100644
--- a/mdformat/_cli.py
+++ b/mdformat/_cli.py
@@ -53,7 +53,8 @@ def run(cli_args: Sequence[str]) -> int:  # noqa: C901
             if not is_md_equal(
                 original_str,
                 formatted_str,
-                ignore_codeclasses=enabled_codeformatter_langs,
+                enabled_extensions=enabled_parserplugins,
+                enabled_codeformatters=enabled_codeformatter_langs,
             ):
                 sys.stderr.write(
                     f'Error: Could not format "{path_str}"\n'
diff --git a/mdformat/_util.py b/mdformat/_util.py
index cb900075..893ad683 100644
--- a/mdformat/_util.py
+++ b/mdformat/_util.py
@@ -1,21 +1,80 @@
-import re
-from typing import Iterable
+from html.parser import HTMLParser
+from typing import Iterable, List, Optional, Set
 
 from markdown_it import MarkdownIt
 
+import mdformat.plugins
 
-def is_md_equal(md1: str, md2: str, *, ignore_codeclasses: Iterable[str] = ()) -> bool:
+
+def is_md_equal(
+    md1: str,
+    md2: str,
+    *,
+    enabled_extensions: Iterable[str] = (),
+    enabled_codeformatters: Iterable[str] = (),
+) -> bool:
     """Check if two Markdown produce the same HTML.
 
-    Renders HTML from both Markdown strings, strips whitespace and
-    checks equality. Note that this is not a perfect solution, as there
-    can be meaningful whitespace in HTML, e.g. in a <code> block.
+    Renders HTML from both Markdown strings, strip content of tags with
+    specified classes, and checks equality of the generated ASTs.
     """
-    html1 = MarkdownIt().render(md1)
-    html2 = MarkdownIt().render(md2)
-    html1 = re.sub(r"\s+", "", html1)
-    html2 = re.sub(r"\s+", "", html2)
-    for codeclass in ignore_codeclasses:
-        html1 = re.sub(rf'<codeclass="language-{codeclass}">.*</pre>', "", html1)
-        html2 = re.sub(rf'<codeclass="language-{codeclass}">.*</pre>', "", html2)
+    ignore_classes = [f"language-{lang}" for lang in enabled_codeformatters]
+    mdit = MarkdownIt()
+    for name in enabled_extensions:
+        plugin = mdformat.plugins.PARSER_EXTENSIONS[name]
+        plugin.update_mdit(mdit)
+        ignore_classes.extend(getattr(plugin, "ignore_classes", []))
+    html1 = HTML2AST().parse(mdit.render(md1), ignore_classes)
+    html2 = HTML2AST().parse(mdit.render(md2), ignore_classes)
+
     return html1 == html2
+
+
+class HTML2AST(HTMLParser):
+    """Parser HTML to AST."""
+
+    def parse(self, text: str, strip_classes: Iterable[str] = ()) -> List[dict]:
+        self.tree: List[dict] = []
+        self.current: Optional[dict] = None
+        self.feed(text)
+        self.strip_classes(self.tree, set(strip_classes))
+        return self.tree
+
+    def strip_classes(self, tree: List[dict], classes: Set[str]) -> List[dict]:
+        """Strip content from tags with certain classes."""
+        items = []
+        for item in tree:
+            if set(item["attrs"].get("class", "").split()).intersection(classes):
+                items.append({"tag": item["tag"], "attrs": item["attrs"]})
+                continue
+            items.append(item)
+            item["children"] = self.strip_classes(item.get("children", []), classes)
+            if not item["children"]:
+                item.pop("children")
+
+        return items
+
+    def handle_starttag(self, tag: str, attrs: list) -> None:
+        tag_item = {"tag": tag, "attrs": dict(attrs), "parent": self.current}
+        if self.current is None:
+            self.tree.append(tag_item)
+        else:
+            children = self.current.setdefault("children", [])
+            children.append(tag_item)
+        self.current = tag_item
+
+    def handle_endtag(self, tag: str) -> None:
+        # walk up the tree to the tag's parent
+        while self.current is not None:
+            if self.current["tag"] == tag:
+                self.current = self.current.pop("parent")
+                break
+            self.current = self.current.pop("parent")
+
+    def handle_data(self, data: str) -> None:
+        # ignore data outside tabs
+        if self.current is not None:
+            # ignore empty lines and trailing whitespace
+            self.current["data"] = [
+                li.rstrip() for li in data.splitlines() if li.strip()
+            ]
diff --git a/mdformat/plugins.py b/mdformat/plugins.py
index 3e5092b1..1fb56e49 100644
--- a/mdformat/plugins.py
+++ b/mdformat/plugins.py
@@ -46,6 +46,11 @@ def render_token(
         """
         return None
 
+    def ignore_classes(self) -> List[str]:
+        """Return CSS classes to ignore when comparing the input/output HTML
+        equality."""
+        return []
+
 
 def _load_parser_extensions() -> Dict[str, ParserExtensionInterface]:
     parser_extension_entrypoints = importlib_metadata.entry_points().get(
diff --git a/mdformat/renderer/_token_renderers.py b/mdformat/renderer/_token_renderers.py
index fe0d2e2f..36b0d12b 100644
--- a/mdformat/renderer/_token_renderers.py
+++ b/mdformat/renderer/_token_renderers.py
@@ -1,5 +1,6 @@
 """A namespace for functions that render the Markdown of tokens from markdown-
 it-py."""
+import logging
 from typing import List, Optional
 
 from markdown_it.token import Token
@@ -12,6 +13,8 @@
     longest_consecutive_sequence,
 )
 
+LOGGER = logging.getLogger(__name__)
+
 
 def default(tokens: List[Token], idx: int, options: dict, env: dict) -> str:
     """Default formatter for tokens that don't have one implemented."""
@@ -101,10 +104,10 @@ def fence(tokens: List[Token], idx: int, options: dict, env: dict) -> str:
         fmt_func = options["codeformatters"][lang]
         try:
             code_block = fmt_func(code_block, info_str)
-        except Exception:
+        except Exception as err:
             # Swallow exceptions so that formatter errors (e.g. due to
             # invalid code) do not crash mdformat.
-            pass
+            LOGGER.warning(f"Code formatting of '{lang}' failed: {err}")
 
     # The code block must not include as long or longer sequence of `fence_char`s
     # as the fence string itself
diff --git a/tests/test_cli.py b/tests/test_cli.py
index ea8c0842..9cdede3e 100644
--- a/tests/test_cli.py
+++ b/tests/test_cli.py
@@ -2,6 +2,7 @@
 import sys
 
 from mdformat._cli import run
+from mdformat.plugins import CODEFORMATTERS
 
 UNFORMATTED_MARKDOWN = "\n\n# A header\n\n"
 FORMATTED_MARKDOWN = "# A header\n"
@@ -63,6 +64,18 @@ def test_check__multi_fail(capsys, tmp_path):
     assert str(file_path2) in captured.err
 
 
+def example_formatter(code, info):
+    return "dummy\n"
+
+
+def test_formatter_plugin(tmp_path, monkeypatch):
+    monkeypatch.setitem(CODEFORMATTERS, "lang", example_formatter)
+    file_path = tmp_path / "test_markdown.md"
+    file_path.write_text("```lang\nother\n```\n")
+    assert run((str(file_path),)) == 0
+    assert file_path.read_text() == "```lang\ndummy\n```\n"
+
+
 def test_dash_stdin(capsys, monkeypatch):
     monkeypatch.setattr(sys, "stdin", StringIO(UNFORMATTED_MARKDOWN))
     run(("-",))
diff --git a/tests/test_plugins.py b/tests/test_plugins.py
index f17572d2..0226b180 100644
--- a/tests/test_plugins.py
+++ b/tests/test_plugins.py
@@ -7,10 +7,35 @@
 import yaml
 
 import mdformat
-from mdformat.plugins import PARSER_EXTENSIONS
+from mdformat.plugins import CODEFORMATTERS, PARSER_EXTENSIONS
 from mdformat.renderer import MARKERS, MDRenderer
 
 
+def example_formatter(code, info):
+    return "dummy\n"
+
+
+def test_code_formatter(monkeypatch):
+    monkeypatch.setitem(CODEFORMATTERS, "lang", example_formatter)
+    text = mdformat.text(
+        dedent(
+            """\
+    ```lang
+    a
+    ```
+    """
+        ),
+        codeformatters={"lang"},
+    )
+    assert text == dedent(
+        """\
+    ```lang
+    dummy
+    ```
+    """
+    )
+
+
 class ExampleFrontMatterPlugin:
     """A class for extending the base parser."""
 
diff --git a/tests/test_util.py b/tests/test_util.py
new file mode 100644
index 00000000..ed058a39
--- /dev/null
+++ b/tests/test_util.py
@@ -0,0 +1,56 @@
+from mdformat._util import HTML2AST
+
+
+def test_html2ast():
+    data = HTML2AST().parse('<div><p class="x">a<s>j</s></p></div><a>b</a>')
+    assert data == [
+        {
+            "tag": "div",
+            "attrs": {},
+            "children": [
+                {
+                    "tag": "p",
+                    "attrs": {"class": "x"},
+                    "data": ["a"],
+                    "children": [{"tag": "s", "attrs": {}, "data": ["j"]}],
+                }
+            ],
+        },
+        {"tag": "a", "attrs": {}, "data": ["b"]},
+    ]
+
+
+def test_html2ast_multiline():
+    data = HTML2AST().parse("<div>a\nb \nc \n\n</div>")
+    assert data == [{"tag": "div", "attrs": {}, "data": ["a", "b", "c"]}]
+
+
+def test_html2ast_nested():
+    data = HTML2AST().parse("<a d=1>b<a d=2>c<a d=3>e</a></a></a>")
+    assert data == [
+        {
+            "tag": "a",
+            "attrs": {"d": "1"},
+            "data": ["b"],
+            "children": [
+                {
+                    "tag": "a",
+                    "attrs": {"d": "2"},
+                    "data": ["c"],
+                    "children": [{"tag": "a", "attrs": {"d": "3"}, "data": ["e"]}],
+                }
+            ],
+        }
+    ]
+
+
+def test_html2ast_strip():
+    data = HTML2AST().parse('<div><p class="x y">a<s>j</s></p></div><a>b</a>', {"x"})
+    assert data == [
+        {
+            "tag": "div",
+            "attrs": {},
+            "children": [{"tag": "p", "attrs": {"class": "x y"}}],
+        },
+        {"tag": "a", "attrs": {}, "data": ["b"]},
+    ]