As long as it is in the terms and conditions, it is completely legal to restrict reselling of tickets. You are entering into a contract with the team when purchasing season tickets (or really any ticket) with the organization selling the ticket. I don't think I ever read my contract when I had season tickets but it is completely legal to restrict.
In the past, it may have been legal to put post-sale restrictions on season tickets. It really isn't anymore. The biggest NFL ST resale case, that I recall, had to do with teams setting a floor price, below which tickets could not be resold. The NFL lost that case.
Essentially the courts are reinforcing the standard that, once sold, the NFL cannot restrict what the buyer does with the tickets, barring them being used for something illegal e.g. as a prize in a non-charity raffle. This is why you see them moving toward non-renewal of tickets. They can't do anything, after the tickets are sold. They can, however, refuse to sell more tickets, if they don't like how you have historically used them.
I'm sure that this will be challenged in court, in the near future. I'm sure it will come down to a question of what the terms and conditions, originally agreed to by the STH, stipulate.
I think a great compromise would be to have a verified Seahawks fans list that STH can sell their tickets to. They already have the Blue Pride list, why not make a specific resale site (linked through the STH website just like the NFL Ticket Exchange is now) that essentially guarantees that your tickets will go to Hawks fans? This allows STH a way to hold on to their legacy, while also filling the stadium with real fans.
As per above, the NFL cannot put these kind of restrictions in place, once the tickets are sold. Perhaps they could add restrictions to the terms and conditions for new STH, but that won't ever deal with the existing problem.
However, they could publish a list of recommended buyers.