Let me get this straight: you would get fired immediately for a picture that depicts a sub-culture of people that is often sexually deviant (but would include no nudity or anything in said picture), but it would be perfectly acceptable to promote a hate/terrorism group whose main purpose is to exterminate large parts of the Earth's population?
It is much easier to win a lawsuit on something appealing to prurient interest since the supreme court says it is not protected.
Most people don't actually care if the people involved in making their products are murderous psychopaths, as long as you aren't putting Nazi symbols in their product or something. That's why what are essentially CCP owned chinese manufacturers run by a party that tank-rolls over people wanting basic civil rights is seen as no-fucking-problem, no one gives a shit and their sales are not meaningfully impacted.
The only reason American employers care is if they're going to get sued, unless they are selling to rich people in San Francisco or something who can afford to pay more to buy something for moral reasons.
Having a sexually provocative furry show up is not protected by the first amendment, since it appeals to prurient interest, someone passing by could argue they feel sexually harassed or find it hostile and have a much better chance at causing problems for your employer.
Maybe I've worked for some weird employers but if I was caught on twitter posting Nazi salutes I would expect raised eye-brows, but for the stated reasons, if I was caught with a furry picture on display where someone else could see it I'd expect to be immediately terminated.