UPDATE: Beeper, through their Twitter account, is saying that they’re working on it and “hope to have good news to share soon”:
Work continues to fix the issue causing the Beeper Mini outage. We know how hard this has been for those who loved using Beeper Mini, and we’re extremely sorry for the inconvenience. We are feeling good, though, and hope to have good news to share soon.
Afaik apple can’t block this without also blocking iMessage on older devices that no longer receive updates.
Pretty sure I saw on Reddit beeper is already working on a fix.
My guess at Apple’s response when they do block them: “Buy a new phone”
This is the company of “you are holding it wrong” after all.