Filling in your comment with Manusmriti doesn't make your point valid.
Now about your comments about Gita.
Bhagwad Gita 18:47 isn't about caste.
Neither 4:13 nor 18:41-43 support your claim of
"that it is actually a sin to perform the duties (dharma) of a caste that you aren't born into"
Bhagwad Gita 4:13[0] and 18:41[1] if anything can be interpreted as varna based on qualities rather than being fixed at birth.
Even bad faith interpretation of these verses does not support your claim.
You come across as bad faith.
[0]: https://www.holy-bhagavad-gita.org/chapter/4/verse/13/ [1]: https://vivekavani.com/b18v41/
Filling in your comment with Manusmriti doesn't make your point valid.
Now about your comments about Gita.
Bhagwad Gita 18:47 isn't about caste.
Neither 4:13 nor 18:41-43 support your claim of
"that it is actually a sin to perform the duties (dharma) of a caste that you aren't born into"
Bhagwad Gita 4:13[0] and 18:41[1] if anything can be interpreted as varna based on qualities rather than being fixed at birth.
Even bad faith interpretation of these verses does not support your claim.
You come across as bad faith.
[0]: https://www.holy-bhagavad-gita.org/chapter/4/verse/13/ [1]: https://vivekavani.com/b18v41/