"Basically no official source anywhere supports the idea Space Marines are actually immortal, just that during the Great Crusade some people thought they might be. That of course doesn't stop anyone having immortal Space Marines in their own version of the background."
Isn't it the other way around?
There's actually official source that say they are... but we've never heard a story of a Marine dying of old age. Ever.
There's a big resistance to the idea that Marines are immortal, most people ballparking their age to 400-500 (When several Marines are already older than that to begin with...Pedro and Marneus for sure, even without any warp travel shenanigans), so obviously the idea isn't very popular... but yeah, as far as I can, the 'offical' view supports immortality.