House is about 100 years old. Been renovated nicely but it shifts like a sob.

Seems seasonal to me. Winter they close pretty well but summer time they get out of whack.

Interior doors are a little annoying but a couple exterior doors don't latch well and on the back door we can't use the deadbolt anymore because it's so out of alignment. Don't like this from a security perspective.

Does some setup exist that is "flexible" to account for shifting? Or am I just going to have to get them adjusted all the time?

Yes, seasonal movement is normal, and this very hot and dry summer is causing a lot more movement for a lot of old houses. The alternative to constantly adjusting things (or dealig with stuck doors) is do have some serious foundation work done that installs piers that go down far enough to become immune to soil shifting.

Edit: A short-term fix is to enlarge the strike plate holes for the latches and deadbolts.

I recently learned about these and it's worked well on some out of whack doors I had.

E-Z Shim EZ HS350BP 3.5" Hinge Shim, 18 count, Pack of 1, White https://a.co/d/j5dj30j

There is a big difference between the house shifting and the door merely expanding in the humidity. If the house is shifting, that is a big issue...

If the house is shifting enough to throw doors out of alignment, you would see multiple cracks in the walls. Typically above door/window frames. You may also see the case moldings miter joints separated.

But if you don't see the cracks, you may merely have doors where the gapping is too tight. 1/16" is about normal, but if the door is very thick, the knob side edge of the door typically has to have a few degrees of a bevel on it to close properly. (Doors these days are 1 3/8" thick, 100 years ago, doors were 1 3/4" to 2" thick.) Shaving the doors is not complicated, maybe a bit time consuming if you have to take the doors off?

And in the places where the dead bolt doesn't fit right, the strike plate may not be seated flush with the door jamb, or the hole may not align with the bolt? Are the hinge plates/screws tight?

Any of these fixes are not terribly complicated, just kind of tedious and time consuming.

Perhaps the hinge shims will work and save time/money! Please report any success with those.

Otherwise, our foundation supporting soils are again acting like a kitchen sponge when it gets really wet or dry = causing your problems.
1. Anchor Foundation stabilizes slabs
2. Painter primes, then paint-seals ALL SIX sides of the doors to bar moisture from warping doors

I'm feeling your pain. Our house is over 100 years old. It is a farmhouse and built and added on to as needed. It is pier and beam. When I say pier, I mean they cut a stump of cedar and put it on the ground and then put wood shins under it. Ours shift as well. The foundation companies want 50k to fix it and get it level which is a huge red flag since it wasn't level when it was built. Your biggest reference is going to be your doors. I use house jacks. You can buy them at Home Depot. When mine got out of whack I identified the part tha was giving trouble and crawled under it and jacked it up until my doors in that part worked properly.

Your doors are probably also suffereing from being to big for the frame. Mine were the same. I took them all off and trimmed a single saw kerf off of the hing side and wherever else I needed to get a gap. Doors, when it gets humid will swell a LOT. I custom built a screen door and sealed it and finished it. It has a solid 1/4" gap all the way around and in the wettest periods, that gap will damn near disappear. It hasn't rained more than 2" here this year so that gap is almost 3/8". You need a decent gap to make sure they work year round.