You won't be able to continue using your Quest 2 if you delete your Facebook account. Have you considered just not using Facebook without deleting the account?
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The problem is even if you find a different way to log on, you are still using a Facebook headset running Facebook software talking to Facebook servers.
To start with, speaking from experience I can attest that Facebook does not delete accounts. Not even when you tell them to delete it. I know this because I told them to delete my account back in 2010 or so. Yet the account still existed when I went to make a new one in 2020 so I could use Oculus Venues.
Second of all, the Quest 2 does require a FB account to use. Like it, loath it, or feel indifferent about it, this is the case. No one is pointing a gun to your head and forcing you to tell Facebook where you live, who your friends and family are, and so forth. You can leave your FB profile blank, enable every privacy option, and never actually use the site.
And finally, were you aware that even if you never signed up for Facebook... they probably already have a profile on you? Not having a FB profile isn't going to keep your private data from them. It just means they didn't get the info directly from you.