Broward has been liberal ever since I’ve been in FL (30+ years). You remember the 2000 election, hanging chads and all. The three counties involved were all lib/dem controlled — Broward, Miami-Dade, and Palm Beach counties.
You may be thinking about Brevard County. It is much more conservative and farther north.
No, I lived in Hollywood, which is smack dab in Broward County.