I think that has a sheer relation with how active the account is and the area of its activity
Seems to be resolved now (at least I can open all profiles again - I don´t know whether the log-in issues still remain).
No, that was not related to activity or on-line status (or alliance/pact alignment).
Might be a coincidence but all the players (friends and enemies) whose profiles I could not open this morning seem to have edited profiles, personalized by using internal or external graphics (such as a list of favourite Grepolisscore awards, pictures) or added personal text, etc.