Some members who tried to register to my forum started to get this error. I tried different browsers and incognito tabs, changed the IP address and still the same error. The user gets this error even though they have never registered before.

In the meantime, there are those who registered without any problems. Why might this be?

This would indicate that the spam service is blocking them. Either because they are in our database as a spammer, disposable email, or the GEOlocation blocks that you have put forth in ACP -> Members -> Spam Prevention.