Touché on modify the joke to serve your best interest, although it'd probably lose its luster as you'd be disregarding traditionally Jewish stereotypes.
Is this sentence grammatically correct? Please elaborate.
This should be the corrected version, imo.
EDIT to answer further questions as asked in the comments:
One simple error: it should begin
since on here needs to be followed by a noun phrase, and so the verb modify must be used in its gerund form modifying.
More debatably, I would suggest using simple past tense rather than conditional forms:
since the beginning suggests that someone has already modified the joke. It’d probably lose and you’d be disregarding are more natural if the modification is still hypothetical, in a context like:
So depending on context — is the modification definitely made, or still somewhat in question? — the simple past forms might be more appropriate, or the original conditional forms.
Edit: as Rimmer’s answer points out, it should also be traditional Jewish stereotypes, not traditionally, since traditional here is describing the stereotypes themselves, not the sense in which they’re Jewish.