You can reward activities that are perceived to have social benefits without playing favorites. People could still donate to the Red Cross if the donations were not tax deductible, and the Red Cross could still operate if there were no such thing as a tax-exempt organization.

Also, when you say "perceived to have social benefits", whose perception, exactly, are we talking about? If you argue (I'm not saying you specifically are, but many do) that we need to give special benefits to the Red Cross because otherwise they wouldn't get enough donations, you are basically saying that other people's perceptions of what activities have social benefits differ from yours, but since yours is obviously better, you are justified in skewing people's perceptions of social benefit by giving them tax breaks for donating to the Red Cross.

Even if we leave aside the question of what justifies skewing other people's perceptions, in a sane world, you wouldn't have to do it anyway. People's perceptions of the social benefits of various activities would be sane, i.e., reasonably accurate, so you wouldn't have to trick them into paying for things they otherwise would not pay for--more precisely, doing so would be a net loss to society.

(I'm not sure it isn't a net loss to society even in our actual world, because I think most organizations that take advantage of tax-exempt status are not doing things which are as obviously beneficial to society as the Red Cross. But that's a different discussion.)