"taxis generally can't refuse transportation to you"
The fact that it happens says nothing about whether it's right or not. In my opinion it's wrong and immoral that taxis can't refuse to service you. But taxis are very regulated in many places. In fact, for example, Uber is illegal in Colombia. And still, despite their legal status, Uber is not only very used in Colombia, but it's also safer than getting a normal taxi.
When there's a big power imbalance, putting the onus on the service provider to give a valid reason for denying customers can be more impactful than laying the burden on a user to prove there was discrimination.
Depending on your race/ethnicity/disability/socioeconomic status, taxi drivers might refuse service even though it is against the law. It is easier to win against a taxi driver if they're obligated to explain why they didn't help someone in a wheelchair.
I respectfully disagree because that goes against individual freedom. I understand that historically in the US there's been racism but that's no reason to erode individual freedom.
A corporation is not a person, though. It is a "legal person", which is a really unfortunate term precisely because it confuses the matter of natural rights and freedoms.
Now, I would agree with you if we were talking about individuals. In that case, yeah, I think you should be able to refuse service for any reason or no reason at all to whoever you want. But if you go and get a corporate charter from the government that, for legal and fiscal purposes, creates an entity that is distinct from you-the-actual-person, then I don't see any problem with the same government telling that distinct entity what it can and cannot do. That entity has no natural rights.
The fact that it happens says nothing about whether it's right or not. In my opinion it's wrong and immoral that taxis can't refuse to service you. But taxis are very regulated in many places. In fact, for example, Uber is illegal in Colombia. And still, despite their legal status, Uber is not only very used in Colombia, but it's also safer than getting a normal taxi.