Can a senior with a homestead exemption who can't pay the HOA dues be legally evicted from the home with a reverse mortgage on it?

Well, it is a foreclosure most likely, not an eviction. Yes, a home can be foreclosed upon. More facts are needed.

Yes, a homestead may be foreclosed by an HOA. Florida's constitution provides several exceptions to homestead protection. Voluntary liens (ex. mortgage and HOA), mechanic's liens (ex. contractors who work on the home) and tax liens (ex. county tax collector) are the general exceptions to homestead protection. Home owners associations are able to foreclose because you agreed they could when you bought the home and agreed to the comply with HOA rules and regulations.