Does it matter which wallet I use? And other compatibility questions.

This Mandatory Upgrade request leaves me with more questions than answers. From what I understood, wallets, nodes, and miners were three separate things. But they're saying I need to update my wallet? Long story short, I have a coinomi wallet but don't want to be in a situation in which I wouldn't be able to use the coins.

Btw, I read elsewhere that exchanges and other users would need to update their wallets. Why would they need to do this and is this related to the soft-forks? Will their coins be trapped forever if they don't upgrade? Sorry for asking all these questions. I just.. Don't know where else to go.