Board Game Arena

Is it possible to block someone you would prefer not to play in Arena mode, and if so, is that fair play?

This would be a site-wide question rather than a specific game question, but no I don't think it's possible.
You could try just red-thumbing a player. The FAQ for red-thumb says you would not be able to meet that player outside of a tournament, but doesn't specifically say that Arena is a tournament for this purpose.

As to it being fair... Well if you're doing it to avoid a tough opponent, then that would seem unfair. If you're doing to avoid a toxic opponent, even if they turn out to be tough as well that seems ok. But ultimately I don't think the site is set up to let you do it anyway.

Thanks. There are a couple of players who I think have me blocked in the Arena somehow. Why, I won’t speculate… I hope I’m not toxic!

There are two reasons I think I’m blocked:

1) I haven’t been matched with them in a very long time, even though we all play games in the Arena frequently.

2) when I click on their profiles, they are the only two players for whom I cannot see the games they are currently playing. For everyone else I can view how many games they are currently playing and when I click on it, I can view their games live.

If I am indeed blocked, I’m not offended… but it doesn’t seem fair to be able to avoid players in Arena mode.

Looks like you were right; General Chat.
That's quite a surprising fail on the functionality, allowing people to bypass tough opponents. I play a lot of arena games and my bronze level rating often gets me put up against top 10 players. I'd assumed this was mostly caused by low population turn-based games, but if there's a lot of use of red-thumb avoidance, it might explain some of it. People end up with no one else to play against.