I provided my XPUB and YPUB to Trezor support - should I continue to use my Trezor? I have a Trezor.  In attempting to find out why I have have not received Bitcoin Gold coins Trezor Support asked for my XPUB - I gave it to them along with the YPUB too.  Is this safe?  Should I move my coins?  Your help is greatly appreciated.
XPUB refers to an extended public key, and because it is only a public key, you have not compromised your private keys. Thus it is safe to continue using, yes. You have, on the other hand, compromised your privacy, as with that xpub Trezor support can derive all your addresses and know they are all yours. But it's likely they just want to look to see if you have any bitcoin gold balance on any of them, it's probably completely harmless