No they don't. Show me in the Constitution. YOUR rights do NOT trump my rights. I buy it, then I get to decide what I do with it and where to park my car, that is, if you live in a free society and not communist.
When you buy into a neighborhood with a HOA it is no different than choosing to move to a liberal state with high taxes and regulations.
You CHOOSE to live there, so you can’t complain.
Would be like moving to San Francisco and then complaining about all the gays.