Most players using altered tunings live are of the folky or percussive finger style persuasion retuning is all part of the show and most chat over it (which takes practice), IME it's rare to see them swapping guitars.
WRT tunings generally, most impart a particular character/tonality so you probably wouldn't use the same tuning for more than a couple of songs unless you are the Dobro player in a blues/bluegrass band or something similar where that tonality is a characteristic of the genre.
BJG145 mentioned the Spider Capo, I use one of these (pic below) to simulate DADGAD* on a few tunes. It's just as quick to use as a standard capo and lets you get a DADGAD (or A maj) tonality while in standard tuning. It capo's the 2nd, 3rd, & 4th or 3rd, 4th, & 5th strings, used at the second fret on the bass side it gives you EBEABE (DADGAD a whole step up). Anything you play above the second position is in standard tuning so barre chords and melody lines that don't use open strings remain as normal
https://shubb.com/product/partial-capo-c7/edit to add:- if you are using an altered tuning on an electric it is often for slide which requires a different setup so a second guitar is more or less a necessity.
* A 'Drop D' version also exists which skips the low E but capo's 1-5