And as it states there, they also have censorship based on their terms of service, where they prohibit the posting of videos which violate copyrights or depict pornography, illegal acts, gratuitous violence, or hate speech.
Reddit isn't refusing to service people because of their ideology or background, they are limiting certain kinds of speech. A private organization is entirely allowed to limit certain kinds of speech.
Way overbroad interpretation. The Civil Rights Act prohibits refusal of some kinds of service based on race, color, religion or national origin, and it's pretty much the only national law (in the US) that's relevant here (I'm not counting the 14th amendment or more specific laws e.g. for disabilities).
Notably, there's no federal law protecting supporters of gay marriage. They're state-specific laws, and not at all universal.
Ideology isn't a protected class. Sexual orientation is, at least in some states.
Regardless, you are not refusing anyone service - you are not banning people from your platform, you are designating your platform as something not be used for certain purposes.
Except it's not that simple. There's a substantial amount of judicial precedent that you can't refuse service to customers just because you disagree with their ideology or background, otherwise it would be okay to refuse service to supporters of gay marriage for example.
It's appalling that you would even suggest that.