I can't speak to all internet forums, but I can speak about this possibility for this site.
Except for a few that have used their real name as their username, tracing you down based off of your participation/membership on this site would take a lot of effort on behalf of the .gov. The staff doesn't know your real names. There are a coupe of ways to identify you if they wanted to put in the leg work, but it'd be time consuming, high effort and, short of a court order, a huge Constitutional violation.
ETA: Places like New Zealand have a long history of not respecting individuals natural rights, particularly as they relate to firearms. It's become much worse over the last 10 years. More proof that elections have consequences and choosing your vote wisely can have deeper ramifications than simply keeping people like "orange man" out of office.