Leaving aside the moral issue, practically, you will be in a much worse situation in the future if a few weeks or months from now a new employer discovers that you were fired from your previous position, and then fires you for lying about it. This is extremely unfortunate, and it appears from your description of the circumstances of your firing, extremely unfair.
You should definitely seek legal advice regarding your firing. I realise that at the moment, the expense of a lawyer may appear to be impossible, but in many areas there are a variety of free or heavily subsidised legal services available. Call a few lawyers, you may find someone who will offer you a free consultation (I always like to know what my options are, if the lawyer believes you have a strong case, you can decide whether to try to find a means of pursuing it). I am guessing you are American, I can’t recall exactly the rules on legal fees in the US, but you could see whether you could find someone willing to work (at least in part) on the basis of a contingency fee - meaning that if your case was successful, you would pay the lawyer a percentage of the money you received in compensation. Why not contact the ACLU? You probably do not always see eye to eye with them, but they may be a resource. Also look for religious organisations that advocate for the rights of people of faith (you may find some Protestant organisations who would be willing to help you), or for Catholic lawyers in your parish who may be willing to give you some advice. Did the company that fired you have a method of filing internal human rights complaints? If so, see if you can still file a complaint. As someone else said, document, document, document. Start now, write down everything you remember. If you file a complaint, keep a photocopy of it in your own files, make notes of any telephone conversation you have (date, time, who you spoke to, detailed notes of what you discussed).