Unfortunately, the U.S. Constitution does not apply to these non-governmental governments, to the best of my knowledge. They do have to abide by certain governance rules, but Home Owner Associations are free to restrict many liberties. And in fact they often violate even the governance rules.
My local paper has a real-estate law column. At least half the questions deal with HOA boards acting without due process. There is something about serving on these small quasi-governmental bodies that makes people into little tyrants.