Rome free first Sundays

Have you checked the individual websites for each museum you are interested in?

Last I knew, Free 1st Sundays had been discontinued awhile back, at least temporarily, for the Italian STATE museums and have not been reinstated. They have reinstated them for Rome's CIVIC museums, however. That is stated here (#2) on this page of the website for this particular group of museums:

http://www.museiincomuneroma.it/en/informazioni_pratiche/condizioni_di_gratuita_e_riduzioni

And it states here that prior bookings are not longer required for these days, although I would check their individual sites to see if that's true for special exhibits.

http://www.museicapitolini.org/en/node/1009525

The complete list of Civic museums is here:
http://www.museicapitolini.org/en/infopage/musei-comune

And just as a side note, those free 1st Sundays at the STATE museums had been largely done away with during high season (April - Sept.) back in 2019 or so. As I recall it, they were each given 8 free days to use at their individual discretion plus culture week. Then COVID hit and, well, we'll see if free days ever make a return appearance in a future year?

Actually the first Sunday free is not the best option. We have learned from experience to avoid them. The locals are not stupid and there are a lot more of them than tourists. The end result is that the frees sites are absolutely packed with long lines to get in. We might attend an open-air, outside event with lots of space but anything inside a building will be packed.

True, "Free Sunday" attractions were best avoided due to long queues and crowds!!! At least that rang true for the tourist-magnet State museums, back when they were included. Some of the lesser civic attractions in winter? Maybe not the case?

Editing to add:
Parco archeologico del Colosseo (also an official site for the attractions that fall under its protection) notes under their FAQs that there are currently no free Sundays for the Colosseum/Forum/Palatine.

https://parcocolosseo.it/en/visit/opening-times-and-tickets/faq-tickets/

And while it doesn't affect the OP. free Sundays at the Vatican Museums (traditionally the last Sunday of the month) have also currently been suspended.

https://www.museivaticani.va/content/dam/museivaticani/pdf/pop_up/covid_musei_vaticani_en.pdf

I guess my opinion is along the lines of a couple others, if they still are in effect, generally trying to visit a major site on a free day is more frustration than value. It would be a good opportunity though to check out some much lesser sight that the crowds would overlook, even something that may not be very high on your list, or may not otherwise bother for the cost.

In a broader sense, yes, you need to verify things due to covid. Things like the free days were affected, weekends in particular may require pre-registration, other sights, like the Pantheon, that was just wander in with no lines, now have to check green passes and limit crowds...meaning lines are now long during the peak of the day.

We just got home this week from a week in Rome, and used Rick Steves’ guidebook as a major reference. He says, unequivocally, DO NOT go anywhere with free admission on a free Sunday. It’ll be so crowded that you won’t see anything.

Some museums were closed on days when they were reported as going to being open, and vice-versa, and hours were sometimes different too, so do t be surprised if something’s not open when you expect. Or the other way ‘round. Paying the admission price assures you a bit of elbow room. Guided tour groups made sone places pretty busy. Gangs of people on a free Sunday would be even more crowded.

COVID precautions are affecting admission policies. The Pantheon, although free, requires an online reservation for admission.