BUG: Inconsistent ordering of rows when merging with how=left and how=right

[pandamatic]

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• (optional) I have confirmed this bug exists on the master branch of pandas.

---

Note: Please read this guide detailing how to provide the necessary information for us to reproduce your bug.

Code Sample, a copy-pastable example

import pandas as pd
df = pd.DataFrame({'a': [1, 0, 1]})

df.merge(df, on='a', how='left', sort=False)

	a
0	1
1	1
2	0
3	1
4	1


df.merge(df, on='a', how='right', sort=False)

	a
0	1
1	1
2	1
3	1
4	0

Problem description

Order of output rows should be the same for how=left and how=right in this case.

Output of pd.show_versions()

INSTALLED VERSIONS

commit : None
python : 3.8.2.final.0
python-bits : 64
OS : Linux
OS-release : 4.14.181-140.257.amzn2.x86_64
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : fr_FR.UTF-8
LOCALE : fr_FR.UTF-8

pandas : 1.0.5
numpy : 1.19.0
pytz : 2020.1
dateutil : 2.8.1
pip : 19.2.3
setuptools : 41.2.0
Cython : None
pytest : 5.4.3
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 2.11.2
IPython : 7.16.1
pandas_datareader: None
bs4 : None
bottleneck : None
fastparquet : None
gcsfs : None
lxml.etree : None
matplotlib : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 0.17.1
pytables : None
pytest : 5.4.3
pyxlsb : None
s3fs : 0.4.2
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
xlsxwriter : None
numba : None

[simonjayhawkins]

Thanks @pandamatic for the report. #33554 maybe related.