Is there any way to set it so that sims never automatically change their outfit (like, even when they're sleeping)? I want a sim to just keep their everyday clothes on all the time; I was hoping that Master Controller would have an option for that, but if it's there, I can't find it.

I don't think that there is a way to make a Sim never change clothes, but what you can do is to set the same outfit for every clothing category. In MasterController there's a command to copy outfits and transfer that between all categories. So you can transfer the Everyday to all available categories and then delete all the other outfits. Then a Sim will change clothes but change into the same that it wore before.

That sounds like a pretty good solution; the only problem is, the not switching outfits is only a temporary condition, so I don't want to delete the outfits from the other categories. Is there any way to just reorder them so that the copied outfit is the default in each category, or do I just need to delete the other outfits and recreate them later?

What happens when you copy an outfit to another category is you add it as a second outfit, i.e. Formal 2. When they automatically change into an outfit they change into the first of the category, i.e. Formal 1 but if you tell them to change into Formal 2 it sets it to being Formal 1 so now when they change automatically they'll change into the old Formal 2 and the old Formal 1 is now Formal 2 where it will be stored out of sight until you want it again. (It sounds confusing but if you play with it you'll see what I mean. )