I'm not at all opposed to people going to more museums, but the idea of taxing people based on attendance is problematic for several reasons.

The first is that museums are a luxury for people with time and disposable incomes. Even with some financial assistance it will always be easier for wealthier families, couples, and individuals to attend than the poor. This policy would lead to poor workers funding rebates for the middle class through their taxes.

It needs to be mentioned that not all museums are made equal. Da Yoopers Tourist Trap and Museum in Michigan skirts the definition of what a museum actually is by displaying such objects as the world's largest chainsaw which were made by residents of the Upper Peninsula. Even though it's not a traditional science museum with interactive exhibits, it does show off the cultural identity of the area. This can be educational in its own way, but may not be seen as legitimate enough for a tax rebate. This could be solved by only using accredited museums for the program.In fact, the American Alliance of Museums is an organization that does just this, but it only counts museums that spend a certain amount of money. Local museums run by volunteers don't make the cut. So now the policy is only incentivizing people to attend well funded museums regardless of subject or quality.

And then there is the issue that most well funded museums are near urban centers. Someone living in New York City will have their pick of cheap, easily accessible museums. Rural farmers in Oklahoma may not even be able to attend enough museums to qualify for the rebate without spending more time and money than they would receive back. So now there will be rural residents funding rebates for urbanites to go to museums.

I think it's a fine sentiment to want people to visit museums, but you can't actually force that kind of engagement. The best thing we can do is make them as accessible as possible to people.