You can build the lower levels of factional barracks anywhere; higher levels require progressively more homeland-type governments, until you can only build level 5 factional MICs in a gov1 province. It works inversely for regional MICs.
That said, in many cases there's absolutely no point in building a factional MIC outside your homeland - for the Romani in the pre-Marian period outside of Italy, for example, if memory serves - because of the AOR restrictions. Same thing in reverse for regional MICs. Of course there's a large transition area.
However, the troop types available are determined by the MIC level and the AOR, not by the government. The government just determines what MICs you can build.