I have no issue with inserting myself into a character if they're somewhat likable, so I don't mind a game displaying some of the MC's thoughts, even if they aren't what I'd personally think - I get that I'm just playing a character, not myself. It's ideal if there are at least some choices on that though, whether it be the ability to pick a personality or just the thoughts.
I don't want to see other character's thoughts unless the main character is a mindreader. Let me guess at motivations and goals, keep some illusion that they are actual people that take some effort to figure out. Especially if they're supposed to be complex, mysterious, or inhuman, I absolutely do NOT want to hear their thoughts and it's just 'I want his dick.'
That all said, it really depends on the game. Mass Effect did a pretty good job of never really showing thoughts, but Shepherd still had a personality you could alter. Something like Witcher has a very defined character with significant thoughts and personality, and it clearly worked for them. I don't think there is one correct answer, just different valid choices.
Most of it comes down to execution.