Actual governments, with the people's mandate, are the only ones with authority to set the laws. Not tech monopolies.
A store is absolutely allowed to refuse service. You're not allowed to walk in to Costco without a Costco card. Plenty of restaurants and clubs have a dress code. Most places have "No Shoes, No Shirt, No Service" rules.
No, that is not true for all private services.
For example, common carriers have strong restrictions on their ability to refuse service to others. Common carrier laws aren't particularly controversial.
These existing common carrier laws could be expanded to apply to other things.
So you cant just straight up dismiss the idea that we should consider requiring a few more businesses to fall under our existing and uncontroversial laws common carrier laws.