The GA is unquestionably aviation related. However there's a lot of GA businesses in the North-East and North-West sectors already so I can't see that it's a huge issue for them to be located there.
IMO either the museum is a charity (in which case it isn't a business at all) or its business is collecting cash from museum visitors. Which isn't aviation related.
I would guess it must have paid a hefty rent for its premises - presumably the airport have a compelling business reason to forgo that.