First a couple of general thoughts:
Despite some major issues with the importing of post-1110 info from GURPS Sword Worlds (and the lack of acknowledgment for the authors of that book although I am sure there are legal reasons for that) the MGT1 Sword Worlds is mostly excellent.
The one thing - and from reviews I am not alone - I didn't like is that MGT Swordies seem just way too Viking and that it is a bit silly imagining people wandering around with battle-axes and byrnies in the 56th century.
The GURPS book I think got this just right - the Aesirism and Sagamaal are there but is not taken to extremes.
After all why should the 56th century descendants of 41st century Scandinavians (and Germans and Vilani) be any more (or less) religious than their 21st century Scandinavian ancestors are now?
Aesirism should be there in the background just as Christianity is in current day Scandinavia and Germany - a smallish minority live their lives by it, a larger minority pay literal lip-service, the majority are atheists, agnostics or have their own pick n' mix belief system but are to some degree culturally influenced by Aesirism without regarding themselves as Aesirists.
So yes bigger settlements will have an Aesirist shrine and cities a temple (and possibly a neo-Lutheran church and a Islamic mosque - there being significant Muslim minorities in Germany and Sweden now - etc) and there will be some clergy identifiable by runic medallions or whatever but you don't really need a whole career for them.
In fact what might work would be an add-on career like the Solomani Monitor and Home Guard options in Classic and Megatraveller - your typical Aesirist doesn't spend whole terms just Aesiring but does have a bolt-on parallel semi-career which gives him maybe an additional 0- or 1-level skill per term served in their real career, a chance of an Aesirist life event and maybe an additional benefit roll or two.
And if this gives the Aesirist PC an unfair advantage vis a vis characters not getting those extra skills make them pay a tithe of 10% of all their income and have them occasionally forced to go off and do a special mission for the local shrine.
(The same principle should also I think apply to Psions particularly in the Imperium where nobody can plausibly be a full time psionic adept or psi-warrior or even wild talent).