I would say that you are not allowed to use their site as a logged in user (i.e. upvoting, downvoting, commenting, making posts).
It does not seem logical to me that Reddit could "ban" anyone from using their public frontends as anonymous users.
They could only do something like that, in my opinion, if access to all their content was gated behind a login.
It's already there:
"By using the Services, you state that: . . . You have not been permanently suspended or removed from the Services."
They have in other ways, too: "No one under 13 is allowed to use or access the Services." That's literally a prohibition from using Reddit, even anonymously.
Furthermore,
> By accessing or using our Services, you agree to be bound by these Terms. If you do not agree to these Terms, you may not access or use our Services
That right there already says you're legally prohibited from using Reddit, even without logging in, if you don't agree to the terms. It's like how I can say "if you don't agree with the rules of my house, you aren't allowed inside."
Why do you think you have a legal right to use someone's service if you don't abide by their rules? Because they "left their front door unlocked"?
Don't give Reddit ideas.
If I ban you from my house and you show up in disguise, you may be able to get in, but you are still not entitled to be there.