Why would putting down "pagan" be a problem?
It wouldn't be a problem for me, but if, for example, you were applying for a job it might present a problem. Even though employers are not supposed to discriminate based on religious convictions, some still do. In South Carolina, some employers are devout Baptists and would be unlikely to offer a job to someone who identified themselves as a pagan, or an atheist, or Jewish, or Muslim. Or even Catholic! I once had a woman refuse to even rent me a room because I told her I was not religious. If I'd said I was a Pagan, or Satanist, I'm quite sure she would have called the police.

I do not quite understand. Why would a working place be interested in your religion in the first place? Unles there were special circumstances.
If there is freedom of religion, why even ask???