The basic thing here is that 1) we can guess from pretty basic physics that black holes have an entropy. 2) in order for a black hole to have an entropy it must have microscopic degrees of freedom. 3) String theory is one of the few ways we've ever come close to actually calculating from microscopic degrees of freedom the entropy we "know" black holes should have. I think most physicists, even string theorists (perhaps them more than others) understand that there are physical and philosophical problems with string theory, but I think most folks also think its the closest thing we have to a working theory and that it is probably a useful language in which to cast certain calculations in lieu of a more complete or rigorous theory.

I'd also like to point out that the actual total funding for string theory is extremely tiny compared to scientific research funding in general since it is a theoretical discipline with very few practitioners. If you want to attach inefficiencies in scientific funding, the LHC is a much better target. I'm a physicist and have an interest in theory, and even I think that we spend too much money on particle accelerators given what we stand to learn from them and the other pressing problems the human race has. I'd be delighted to see all that money re-allocated to large scale public works building solar panels and infrastructure or just giving it to poor people.