Yes, you could be terminated for doing something the employer doesn't agree with, just like you could quit and start your own business to compete with the employer.
In Florida, employees are presumed to be "at will." At-will employees may be terminated for any reason, so long as it's not illegal. Generally, employees who work under an employment contract can only be terminated for reasons specified in the contract. In Florida, it is very difficult to overcome the at-will presumption.
In Florida, you can be fired for anything as long as it's not one of the following reasons. Employers are not allowed to terminate or discriminate against employees for age, race, sex , religion, national origin, disability or pregnancy.
It's also illegal for an employer to terminate an employee for refusing to break a law, in retaliation for filing a discrimination or safety claim, for taking leave under the Family and Medical Leave Act, without following its own stated procedure or policy, or for reasons not contained in the employment contract, if one exists.
Hope this answers your question.
Zonald Spinks, Esq. Phone: (813) 413-5352 Fax: (813) 658-5893 Twitter: @ZonaldLaw Skype: Zonaldlaw Disclaimer: legal information is not the same as legal advice -- the application of law to an individual's specific circumstances. Although we go to great lengths to make sure our information is accurate and useful, we recommend you consult a lawyer if you want professional assurance that this information, and your interpretation of it, is appropriate to your particular situation. This information is not intended as legal advice for an individual situation, it is only provided as information.
The short answer is yes.
The longer answer, as the other poster noted, is that you can be legally fired in Florida for a good reason, a bad reason, or even no reason. There are various laws that prohibit workplace discrimination and retaliation for engaging protected conduct, but based upon your limited facts, it does not sound like any of those are implicated.