Missing key info about what you trying to do, what is getting broken, how is broken, etc, etc.
Having to guess:
Are you really selecting the actual object you want to move? (move thumb finger having selected any other random object like right knee), in which case, make sure to select the item on the timeline interpolable, then click the corresponding keyframes you want to edit then use current value.
Do you actually have the right object selected, but not the right interpolable selected? (Select right knee to move, but having thumb01_L selected on the interpolable), in which case, just make sure to unselect whatever you have selected on, and just clic the interpolable you want to edit, if there's none, add them scrolling down the timeline if there's allready the body part/object build it, if not, install shalltyutils, (dunno if works without it, haven't tested nor care enought to search for), reopen the scene, open timeline, keeeeep scrolling till you find "GO" or "KKPE"" and middle clic the axys you need to move, you may have to play around with it to make edits, but once you played with it over time will be faster than figure it out why tf the hand doesn't move and get piss off because you wasted 6 hours trying to fix a thumb crawling/clipping a tit, quit and try again for like days till a friend fix it for you (never had it happen, don't look at me)
Is the workspace have some sort of object adjustment and you just not edit them but the body/object itself? (sometimes, creators have this cute thing to help adjust/offset certain body parts/objects), in which case, use them instead of the object itself, they have keyframes so easier to edit.
Are you using node constraints? (link object with object making annoying to edit keyframes so most of the time is ALL IN on it), in which case, CONTROL + i and there's 3 boxes, top one are the axis, middle one the links already setup and bottom one the nodes, in our case, middle box, clic all elements there, you want to verify not linked things to whatever you trying to move, if is the case, I'm sorry but wont help you on that, I hate node constraints with my soul, got a commission with a scene with shittons of them, just manage to make at least 1 work (AS YOU WANT TO) is a pain in the ass, is pretty simple to use if you just turn your brain off and there's like a few linked so not really a big deal, I wish to you to learn more about node constraints, may help your projects a lot, just don't be all monkas with it, lord have mercy on me and this poor soul about to trynna enter node constraints nah jk.
I was playing with the scene you provided, changed character a lot of times, crazy on timeline and haven't found any issues with it, maybe I'm not moving whatever you moves that breaks the scene:
Did video of them, soft handjob with happy ending and CRAZY fast one, if I dare to upload say hi that's me
Would love to help you-best regard