The answer is, they probably can. But that does not mean you lose all rights to complain about how you were fired. Your question seems to put some emphasis on the fact that your ex-employer was a “non-profit.” The most important basic point is that, with several big exceptions (ranging from union shops, military or safety, and some religious organizations), an employer is pretty much an employer. The organization, non-profit or not, usually has to follow the same general rules as every other employer in the state where you were working for them.
 
The most likely place for you to prove you should not have been fired will be in an Employee Handbook. Almost all non-profits have these handbooks, and many courts have ruled that these handbooks are akin to an employment “contract.” Be sure to see if you were on probation (often ninety days). If you can find a written policy on work performance, warnings, or actual termination, which wasn’t followed, then you may have a good case for breach of contract.
 
If there’s not an Employee Handbook, most of the answers to your question will have to do with Louisiana state labor rights, and possibly (under even fewer circumstances) federal protections such as the Americans with Disabilities Act (ADA). If you have a disability that relates to why you were called “disruptive” you may have an ADA complaint. http://www.advocacyla.org/.Usually the employer has to actually know of the disability. But before we look at employment laws, let’s quickly discuss the matter of “non-profit” employment. We’re going under the assumption that you were a regularly  paid or salaried employee, and not an intern, volunteer, or board member.
 
Does Being “Non-Profit” Matter?
 
One thing that would be helpful is to know whether this was a state or federally (IRS) recognized “non-profit.” The reason for this gets kind of complicated, but it goes to understanding exactly how the non-profit runs. Many people use the phrases non-profit and “not for profit” very differently. Sometimes, a non-profit may have some special operational rules. They may have been established as part of a religious group or special government-affiliated association. Sometimes, this can allow for employment practices that are different from a more traditional employer. In other words, if your “disruptive behavior” was undermining their special status or practices, then they have more justification…just so long as these special rules were sufficiently explained to you before you started.
 
If, however, you feel that at the end of this process, the non-profit is not acting in a way that’s fair or consistent with its non-profit mission, then you can try to do something about hat, too. It may not help you get your job back, but it may make the organization learn something. A non-profit needs to operate either under a state business license ( Form # 395 http://www.sos.la.gov/tabid/814/default.aspx) or from the IRS. Soliciting donations without having received legal non-profit certification might be fraud. You can get a full profile about your ex-employer’s organization from the Louisiana Secretary of State at the above address.
 
Now, we’re going to look beyond the non-profit point (which probably won’t help your case or even be relevant). Instead, most of your rights come from laws about having specific job rights (usually under Louisiana law) or anti-discrimination laws (under both state and federal laws).
 

• Louisiana State Employment Rules

 
Louisiana is a “Right To Work” state, which means you can be fired for almost any reason at any time. Also, Louisiana state labor laws really aim only at businesses with 20 or more employees; here’s where you can find out about state worker’s rights: http://www.laworks.net/.Put another way, you may still have a civil claim (the right to sue), but the state does not have to help. You may be eligible for low-income legal help: http://www.lawhelp.org/la/statedirectory.cfm.
 

• Federal Employment Rules

 
For the most part, under federal laws, you can look at possible discrimination issues. http://www.osha.gov/as/opa/worker/complain.html.
 
When to bring a complaint…
 
First, write to the employer’s supervisor or department that made the decision. If you want your job back, show that you want to fix the problem. At the same time, you may wan t to include in your letter asking for re-instatement that you will be sending a letter to the Louisiana Workforce Commission. Give that a week and then send your State Commission letter (unless you have a discrimination complaint).
 
Keep focused on your goal. If your aim is to get your job back, don’t “burn your bridges.” Stay cordial and show there was a misunderstanding that won’t happen again. And as you communicate with your ex-employer, also be careful not to go into too many details (or take on blame) that might hurt any case you may have against them.