Husband's Safari favorites appearing on my new MacBook

As I understand your question, you are both signed in to your respective devices with you own unique Apple Account credentials, yet his Safari bookmarks are appearing on your Mac.

Somewhere along the line one of you must have used the other one's credentials, but determining exactly how that happened and how to correct it is likely to require divulging your Apple Account credentials which you should never do on a publicly available website like this one. Fortunately, your Mac is new, and with that purchase you have 90 days of complimentary Apple technical support via phone or chat. I'd avail yourself of the opportunity. You can discuss those personal details with Apple.

Start here: Official Apple Support, or details of that offer you should have received from Apple upon purchasing your Mac with your Apple Account credentials.

I am signed in to both his and my Google accounts on my phone and computer.

That is another possibility. I know enough about Google's privacy intrusiveness to keep it far away from anything and everything I can, so I won't be able to help you on that subject.