Florida is an at-will employment state. This means that employers can generally fire their employees for pretty much any reason. A reason for terminating an employee in Florida can be anything from a performance issue, to budget cuts, to a simple personal dislike for the employee. However, although employers do have a lot of leeway to get rid of unwanted employees, they cannot fire employees in violation of any state or federal employment law.
Discrimination based on a person's sexual orientation is a sad reality in this country. Unfortunately, this happens in employment both in hiring and on the job, and this is not banned by federal law--unlike discrimination on the basis of race, gender, sex and other categories.