I am a fastmail customer in a different region (Poland). I am however looking closely at this as who knows, maybe I will be on the receiving end in the future?
Such customers are probably on their own - but the article does spell out what they've done, so hints at the solution: VPN to outside Russia in order to sort out moving. (Or stay with Fastmail and accept that you need the VPN to use email, I suppose.) The CEO does often comment on Fastmail submissions here (brongondwana) but I suppose maybe not in this (lawyers involved) case.
On top of that there is a question of billing and refunds in the case of long-term plans being paid up front (eg. one year subscription).
> As of the time of publication, there are no changes to other accounts, and email flow in and out of Russia has not been blocked, but we will continue to monitor the situation.