We've been making the move away from disposable paper slowly, over several years. The first big shift came when our kid was born. We invested in some secondhand cloth diapers (though we never managed to be exclusive with it) and I got used to a workflow that involved doing a load of laundry that was mostly diapers, burp cloths and kitchen towels.
As she outgrew the diapers, I discovered that old cloth diapers and burp cloths make fantastic towels for cleaning up spills. They are, by design, incredibly absorbant. Much more efficient than paper towels, and so a stack of old diapers found their way into the kichen cabinet next to the dish towels, and eventually I realized I was only using paper towels when I made bacon. It was so easy to make that switch that I didn't realize we'd done it!
Once I realized that, paper napkins never stood a chance. Since spills and other messes were easily taken care of by the towels and burp cloths, we only needed napkins for fancy table settings. I had no trouble finding lovely cloth napkins for less than $5 at the thrift store (along with a matching tablecloth).
Tissues were another area that was much easier to swap out than I expected. In a worst-case scenario, where I have a bad cold and I'm out of the house for some reason, yeah, paper tissues that can be tossed are probably the way to go. But honestly I don't get colds as much now thanks to masking, and when I'm home, or when it's not a lot of snot, handkerchiefs are not only just as convenient but they are much softer on the nose. Since I'm home, if I use one, I can just throw it in with the towels.
Inevitably when you talk about replacing paper with cloth, the thing people always want to bring up is toilet paper. I'm a notorious bulk-buyer, so back in 2020 when shortages started happening, I already had enough TP on hand to last us a while. But I was also intrigued by the bidet discussions I saw online, and so my spouse and I decided to get one that was a pretty simple install onto the toilet. And once we had a bidet, the switch to using cloth in the bathroom was pretty much a non-issue.
What you DON'T have to do
Be Perfect: I think where people tend to get hung up is that it's easy to feel like you have to be all-in, hardcore, 100% no disposable paper anywhere, and that's really not the case. I still keep a roll of toilet paper around, and a stack of napkins from those places that put a huge handful of them in your takeout bag for the occasional solid-yet-gross mess that sometimes results when you have a kid and a cat, and that roll of paper towels doesn't get touched often but sometimes I'm really glad we have it.
Look Perfect: People sell super cute "zero-was cloth alternatives" online. If you have the money and you want snap-together Unpaper Towels that you can put on your towel dispenser, go for it, but it's not necessary. Heck, matching dishtowels aren't necessary. You can hang up the nice ones and put the others in a drawer, or you can decide you don't care because who's going to judge you, but either way, don't overthink it.
Call It 'Family Cloth': By far the biggest hurdle to using cloth in the bathroom, even with the bidet, was the fact that 90% of the discussion online about making that particular switch is done by a certain kind of Mom Blogger, and that kind of mom blogger tends to call it Family Cloth, and by god do I hate that term for it.
Make Changes That Don't Work For You: Reducing or eliminating disposables is not going to work for everyone- if you take your laundry to a laundromat, you probably don't want an extra load of towels to deal with, and that's understandable. We all do the best we can with what we have to work with. For us, we have a washer, and we already had the rags, and I could install the bidet myself, and I've had the extra-load-habit since the kid was in diapers, so it was relatively easy. What matters is stopping and thinking about the choices you're making instead of taking them for granted.