Uber would just ban his account for life if he pulls this, most likely automatically without any effort to investigate and definitely not going to any courts.
Funny thing is, I'm in a city where Uber is fighting a competition with Lyft. I've already converted six different people with my story. Clearly customer experience and retention is not their priority...
It will only look bad if that person has enough clout to make the story that visible. But most people don't which is why Uber, Facebook, Google, etc. can do whatever they want with your account and offer you absolutely no recourse. The balance of power in these relationships is tilted so much to one side that nothing short of strong regulation will help the regular user.
Now a typical business can probably stop doing business with you simply because they hate you (not your 'kind', just you personally), but can Uber?
They are likely embershed in so many regulatory frameworks that require them to serve the general public fairly, that they won't be able to cut off service simply because you won a lawsuit against them.
I think any private company doesn't have the legal obligation to serve you or many of the rules that apply to public/government institutions. See Cloudflare refusing to serve right-wing extremist websites, or Youtube taking down similar videos and channels. The only justification they need is that you failed to comply with the terms and conditions of the service. The leverage some have is judging them in the court of public opinion.