I wonder if it will affect the mail exchange, or only client access?
According to the article, it sounds like Fastspring themselves blocked customers with Russian IP addresses from signing up, and removed their app from Russian app stores. I'd hope that even if the Russian authorities would block Fastmail, that they would only block their web servers and maybe their IMAP servers, but not their SMTP servers. The latter would impact a lot more people in Russia.
Alternatively, their sign-up form was broken for all users at that time, but I hope they’ve better SREs than that.