To what extent do mobile adaptations of board games change the games?
You are probably going to have to perform more research to find an answer to your question.

Yes, mobile application developers take liberties.
I would guess that few mobile app developers implement variations, official or not. no one is going to waste development time on version 1 implementing a variant that might not be played. (but the only way to verify this would be to find all mobile apps for Boardgames and figure out which of those have game variations in physical form, then figure out what percentage of those have mobile app variants)

Are mobile apps that behave differently received well? Don't know. Do you know of a polling company that does this kind of research? Do you have a list of all liberal implementations of board games, such that a poll could determine that 50% or more of those games were received poorly/well?

I don't think your question can be answered without considerable effort.