There are exceptions to free speech.
The f word is likely one of them.
But that’s why we have asterisks. :-)
george carlin the 7 words you cant say on tv
caution bad laguage:
https://www.youtube.com/watch?v=kyBH5oNQOS0
Not all f-bombs are treated equally. The use of the f-bomb in this woman's case was part of the content of political speech therefore protected under the First Amendment. Using the f-bomb outside of political statements is not necessarily protected speech, depending on the circumstances.
The other issue at play is that since the HOA is a private entity rather than a federal government what extent if any does protection of political speech apply to them. The Supreme Court of NJ ruled on this issue in a 5-1 decision in Mazdabrook Community Homeowners’ Association v. Khan, which found that the NJ constitution limited the HOA from abridging free speech in a blanket restriction on political signs. However they still affirmed the HOA can set reasonable limits on the number of signs and placements.
If the issue was the HOA had some rule about her number of signs, or size or placement the HOA would be within their power. However this appears to be about the content of the speech, allowing some they are agreeable to and disallowing others they are not.