Answer: As seriously as context tells you to. I don't think inflexibility on one thing is automatically a sign of trouble - especially something that you can appreciate as "one of his favorite places on earth," and especially when he (quickly, it seems) volunteered to sacrifice something valuable to create a little more flexibility where previously there was none.
But that simply means you need to air this out more; don't just take your consolation week and like it. If you see yourself wanting to go to the beach with him in February some year, or whatever, in addition to your normal week of family visits, then don't be shy - say it now, and see what he says.
If his answer is "I have no interest in the beach, and the whole time I'd just be annoyed about my lost week in the cabin/lost pay," then you have to take that very seriously as a prediction of life with him. I do hope he'd be that honest with you, if that's how he feels. Speaking a truth that might make us look mean or selfish is far better than saying all the right things and having no interest in following through - yet nerves do falter at truth time.
Even if you don't feel strongly about variety in vacations, you also need to pay careful attention to other non-cabin things he feels strongly about. When people don't care much about an area where their partners are inflexible - say, religion - it's easy to resolve differences by letting the ones who feel strongly have their way. Sometimes, though, the mellower halves go on to find out their mates aren't just dug in on religion, but instead are one-person Maginot Lines of entrenched positions on issues - some of which the erstwhile mellow ones do care about, a lot.
So, try to see as much of the picture as you can before you decide whether this is about a great cabin, which isn't terribly serious, or inflexibility, which is. Make sure the "give" lines up with the "take" - not just his, but yours, too.
Email Carolyn Hax at firstname.lastname@example.org, follow her on Facebook at www.facebook.com/carolyn.hax or chat with her online at noon Eastern time each Friday at www.washingtonpost.com.