j7n,
I registered an account (free plan) at Protonmail a couple of days ago, didn't have to supply a phone number or a backup mail.
I used Mypal 29.3.0, no problems with the captcha test or accessing the mailbox.
Just tried Protonmail with roytam1's New Moon 28(2021-07-30), no problems at all.
You're not alone, maybe some tips here:
https://forum.palemoon.org/search.php?keywords=protonmail&sid=3950fce43da51eb20f292b1030395722
BTW, don't ask any questions there about Pale Moon forks and XP, Moonchild and Tobin will explode...
Thinkpad T43/2 GHz/2GB RAM/Radeon X300/XP Pro SP3/line speed 100/100.
.