I use Firefox (Linux) and Fastmail, and definitely don't have any problems: the web UI is just as fast as always and have no CPU issues. Maybe it's some addon or something?
Can definitely be due to addons. That innocuous Emoji keyboard addon [1] for example, caused horrible page load performance and unresponsiveness (due apparently to parsing the entire DOM in order to replace/insert emojis); filed a bug at [2]. Hope the move to WebExtensions lets Mozilla provide less opportunities for extension developers to shoot users in the foot.
I think you're right about this one. Sorry about that. It seems to have started interacting badly with Ghostery -- which I had been using for years, but which did have an update recently as well. I tried a different ad-blocker and it's been a lot quicker since.
I think I jumped to conclusions because the change roughly coincided with a visible update to FastMail (the one that added the little progress spinners to the folder tree).
I'll add, for the record, that simply trusting the site in Ghostery appears to be enough to speed it up again.
(My earlier post lost a couple of HN points after I posted that reply, even though it was many hours after the original discussion. I wonder whether people had upvoted it because of potentially useful material about Firefox and FastMail and then unvoted when I admitted that particular bit was bogus. It would be rather encouraging if that were the case)
Later edit: I spoke too soon. After editing an email extensively, the whole UI slows down again.
[1] https://addons.mozilla.org/en-US/firefox/addon/emoji-keyboar...
[2] https://bugzilla.mozilla.org/show_bug.cgi?id=1339822