Privacy is hidden content/actions, anonymity is hidden identity
I think both are pretty important because missing privacy leaks data that can be used to unravel your anonymity/psuedonymity over time (what addresses you interact with, amounts, timing, etc)
It's harder than ever now since Samourai and Wasabi are out of the game. And it's impractical to coinjoin every transaction anyway especially as fees climb.
If you don't coinjoin every transaction, aside from third parties, your counter parties will be able to see balances and see past history + follow you going forward. I'm sure people most wouldn't be comfortable with that even if you know the person.