diff --git a/NEWS.md b/NEWS.md
index 30ed7293f..983e3356f 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,6 @@
 # testthat (development version)
 
+* `set_state_inspector()` gains `tolerance` argument and ignores minor FP differences by default (@mcol, #2237).
 * `expect_vector()` fails, instead of erroring, if `object` is not a vector (@plietar, #2224).
 * New `vignette("mocking")` explains mocking in detail (#1265).
 * New `vignette("challenging-functions")` provides an index to other documentation organised by testing challenges (#1265).
diff --git a/R/test-state.R b/R/test-state.R
index ff1320314..6fb878515 100644
--- a/R/test-state.R
+++ b/R/test-state.R
@@ -42,7 +42,8 @@
 #' @export
 #' @param callback Either a zero-argument function that returns an object
 #'   capturing global state that you're interested in, or `NULL`.
-set_state_inspector <- function(callback) {
+#' @inheritParams waldo::compare
+set_state_inspector <- function(callback, tolerance = testthat_tolerance()) {
   if (
     !is.null(callback) &&
       !(is.function(callback) && length(formals(callback)) == 0)
@@ -51,11 +52,18 @@ set_state_inspector <- function(callback) {
   }
 
   the$state_inspector <- callback
+  the$state_inspector_tolerance <- tolerance
   invisible()
 }
 
 testthat_state_condition <- function(before, after, call) {
-  diffs <- waldo_compare(before, after, x_arg = "before", y_arg = "after")
+  diffs <- waldo_compare(
+    before,
+    after,
+    x_arg = "before",
+    y_arg = "after",
+    tolerance = the$state_inspector_tolerance
+  )
 
   if (length(diffs) == 0) {
     return(NULL)
diff --git a/man/set_state_inspector.Rd b/man/set_state_inspector.Rd
index 08ae0740b..61e52f1b1 100644
--- a/man/set_state_inspector.Rd
+++ b/man/set_state_inspector.Rd
@@ -4,11 +4,24 @@
 \alias{set_state_inspector}
 \title{Check for global state changes}
 \usage{
-set_state_inspector(callback)
+set_state_inspector(callback, tolerance = testthat_tolerance())
 }
 \arguments{
 \item{callback}{Either a zero-argument function that returns an object
 capturing global state that you're interested in, or \code{NULL}.}
+
+\item{tolerance}{If non-\code{NULL}, used as threshold for ignoring small
+floating point difference when comparing numeric vectors. Using any
+non-\code{NULL} value will cause integer and double vectors to be compared
+based on their values, not their types, and will ignore the difference
+between \code{NaN} and \code{NA_real_}.
+
+It uses the same algorithm as \code{\link[=all.equal]{all.equal()}}, i.e., first we generate
+\code{x_diff} and \code{y_diff} by subsetting \code{x} and \code{y} to look only locations
+with differences. Then we check that
+\code{mean(abs(x_diff - y_diff)) / mean(abs(y_diff))} (or just
+\code{mean(abs(x_diff - y_diff))} if \code{y_diff} is small) is less than
+\code{tolerance}.}
 }
 \description{
 One of the most pernicious challenges to debug is when a test runs fine