I would imagine the answer to the first question is, well yes of course it is allowed. They own (or have some right) to the property they are lending so they can decide on any number of arbitrary factors whether or not to lend to a particular borrower.
Is it against Airbnb's rules and policies? Actually, from everything I can find, no. This is absolutely fine. You can, as a lender, make any number of "house rules" in a "house manual" as long as you state your rules upfront. Maybe this lender feels that married couples take better care of the house in question. Or maybe they have religious beliefs about unmarried couples. Or maybe they just hate people who are dating. As long as the rules are stipulated up front and not in a rude way, it seems just fine according to the rules.
Now, will this help them lend their place? Hard to say. The market will drive that entirely. But as for "allowed" the answer seems to be a clear, yes.
Seems like they will only intervene if the host doesn't comply with local discrimination laws.So I guess she should find if Norway has any anti-discrimination laws with regards to housing and martial status.
And if it's specified in the listing itself they might intervene regardless of local law if I understand it correctly.