That's just it though by your votes you are deciding how you are viewed...not the other way around. You don't like how they are representing you? Stop voting for them, it is that simple.
No, you aren't. Mature people don't judge the contents of someone's character solely by their voting patterns (that's called guilt by association) especially not in this day and age when politics is conducted for the highest bidder. The only thing this indicates to me is that you have a problem with diversity of opinion. Hopefully I am wrong.
And yes, except for the hate groups you listed, most of those groups are represented in games where the story is broad enough to include them. It's only a few keystrokes or one artist's rendering to add a detail to a character. Obviously not the player character, but I really can't think of a single old or new RPG game that didn't have at least one physically handicapped NPC(usually the wise blind guy trope) and multiple shades and flavors of characters.
What's a hate group? Do you not realize how error-prone and subjective the term is? Most of the movements you call hate groups operate legally around the world because having a particular opinion doesn't make you a criminal (no matter what the news media says) in a society that values free speech. What's stopping me from calling you a hateful person based on your post history? You can't think of a single old or new RPG game that didn't have at least one physically handicapped NPC? Okay, how many wheelchair-bound characters can you think of from recent games?
In summary, your view of diversity seems to be very narrow. It's very convenient to smear minorities you don't like as hate groups, isn't it? Plus, who is supposed to be prioritized (who is at the top of the diversity totem pole) when making things like games according to your opinion?