It's very simple....if you buy a home where a HOA exists, then you agree to abide by the deed restrictions and covenants set by the HOA. Make sure you know what they are before you sign on the dotted line. Don't assume you can just live with them. That does not mean that any HOA anywhere in the USA is permitted to make rules which violate local, state or federal laws. And trust me, some will unknowingly try. HOA's like any other governing body, have a purpose. If you don't want to be a part of that, then don't. It's not for everyone. But the bottom line is that no HOA can create rules or enforce rules that violate the laws of the state in which they reside. Those rules are considered by any court to be unenforceable, or null and void, just as signing a contract (lease) which contains clauses that violate the law are null and void. It's no different than a HOA making a rule that says we don't allow our homeowners to sell to black people. Violates Title IV and would be illegal. And the HOA can find itself smack dab in the middle of a lawsuit. Rules vary by state as to the culpability of the individual members of the board in any suit, but this is all simple private law.
So, if you want a clothesline, make sure they're allowed and/or protected by environmental law....then hang away!!