Is it working as intended for republic vassals (or a modded vassal government with the open elective succession type) to not get married? I tested it out and noticed that the rulers of the Republic of Novgorod don't get married at all, but will willingly accept marriage proposals. I could understand a lowborn character struggling to get married, but even ones with dynasties won't get married. Is there a file I could change so they can get married, and if so which file?
If they're non-merchant republics (meaning they pass the is_republic = yes check but not the is_merchant_republic = yes check), I believe they won't marry at all (likely for performance reasons, since having non-playable republics led by characters actively trying to get married is going to mean more checks than if they simply don't care), and that cannot be modded since the marriage system is hardcoded (well, assuming you're not going to be tearing out the whole system; I really don't recommend that). In that case, your best bet is to have somewhat rare on_X_year_pulse events that make them get married (ideally to a courtier generated out of thin air, since you otherwise have to check a bunch of characters to find a suitable spouse
and need to figure out acceptance logic for the AI).
If you've got a "republic" that's actually a feudal realm (meaning it passes the is_feudal = yes check) or a republic that passes the is_merchant_republic = yes check (even with a custom government type; be aware that modding MRs is extremely difficult due to a lot of things being hardcoded), I
think they would try to get married even with Open Elective. If they aren't, you might want to @ blackninja9939 (I've deliberately left that @ broken to avoid unnecessarily pinging him) to check if it is a bug and report it if it is one (and possibly suggest changing it in the suggestion thread if it is working as intended).