There are literally dozens of ways you can raise upkeep costs by changing civics. If you go from running Paganism to running Pacifism and see a big jump in your upkeep, it's because you've got a lot of military units you're suddenly paying extra for. Similarly, switching out of State Property might lead to an increase in your upkeep because you're suddenly paying distance upkeep costs again. Or switching out of Bureaucracy could hurt your research rate because you aren't getting +50% commerce in your capital any more. And so forth, and so on. The only real advice I can give is to read the in-game descriptions of the civics, because they are absolutely clear about what they do. Also, it's not always a bad thing if your slider goes down when you switch civics. Someone swapping into Slavery from Tribalism will usually see their upkeep rise a little, but the benefits of slavery far outweigh the small extra costs (although it does mean sometimes you put off the swap a few turns until you are ready to actually make use of slavery).