No, in most cases I don't think it restricts a developers creative freedom. If a character's race, gender, religion, or sexuality is of no consequence to the game's story or vision then why not include characters of varied backgrounds. But if a developer feels pressured to change the story or original vision drastically in order to accommodate a groups wishes, that's when I feel it would be restricting.
That Tomodachi Life example is horrible btw because in that case you are playing as yourself in that game. So if you happen to be gay or lesbian you can't properly enjoy it to its full extent as someone who is straight could. Nintendo honestly should have seen that coming, I mean it's a life simulation game after all so you should be able to portray yourself appropriately.
