I just added fire tape to the drywall seams in my 1950s garage using two layers of this compound from USG. I couldn't find any reference to this question in their docs: Do I need to paint over the mudded seams after they dry, or can I leave them exposed? I live in the upper Midwest of the U.S., which sees pretty gnarly temperature swings and humidity levels throughout the year.
No, paint is not required for wall board on combustible (wood) construction. (See ICC Table 720.1(2), Items 12, 14, and 15.)
Note: Item 15 includes 2-hour fire rated construction too (two layers of gypsum board).
However, be aware that nailing requirements, type of plaster mix, etc. do matter. Most stud spacing is 16” on center, but I did see one with 24” on center (14-1.4 ) with gypsum board long dimension to stud, with 6d cooler nails or wallboard nails at 7” on center.