Whenever I try to change my skin (in 1.19.30) it automatically reverts back to the classic Steve skin, also this happens only on logging on to worlds, not on the Home Screen. 

Since the 1.19.31 hotfix release, the way to reproduce this have changed. Now these are the steps:

1) download a bunch of heavy mods (like 4-5)

2) upload them to the world (infinite world type)

3) login to the world

Also, maybe this is just a problem which the system memory, please inform me about it

EDIT 1 : STEPS TO REPRODUCE IN LATEST VERSION
EDIT 2 : ENABLING THE MODS GLOBALLY CAN CAUSE YOU TO NOT SEE THE CUSTOM SKIN AT ALL IN THE ENTIRE GAME AND OTHER PLARES CAN SEE YOUR CUSTOM SKIN NORMALLY.