Vladinir, yes we all spend many years in education and almost everything we learn is correct, so it is easy to put too much faith in the formalisms and extrapolate them to new areas as if things have to work the same way. To do fundamental physics it is important to have a good feel for why we believe in certain things. If it is because mathematical logic or experiment confirms that they are right, then that's fine. If it is just because we have grown used to the formalism then we need to question if it is the right way to go forward.
I think the choice between continuous and discrete mathematics in theories of quantum gravity is a good example. Classical physics gets us used to working with continuous functions and it is only when we do quantum physics that some discrete theory comes in. Even then the formalism is usually portrayed as continuous with discrete aspects arising from solutions to differential equations of bound systems. People who have come through a physics education tend to favour continuous formalisms because that is what they have always used
Some people who are less steeped in physics as their education take the opposite view and think that things have to be discrete ultimately because infinities are illogical. That is not really correct either. There is nothing logically wrong with continuous mathematics or infinity.
I don't know whether the laws of physics will ultimately be expressed using continuous or discrete mathematics but aspects of both seem to be important at our current level of understanding so it is important to keep an open mind.
The Fermi findings which rule out some discrete theories are an important clue that must be taken into account, but so is the holographic principle which seems to point in the direction of discrete bits. We have to find a way to incorporate all the indicators we get.
I don't think that string theorists as a group are close-minded. I don't personally fit the profile of a typical string theorist, but I have talked with some and read the work of others. They all seem willing to consider new ideas. They are just unwilling to look at alternatives to string theory that seem less promising.
There are some powerful arguments that string theory is the right road to quantum gravity. There must be some logically consistent description of the interaction between particles and gravity in the limit of weak fields and almost flat spacetimes. Perturbative string theory is the only solution we have for that. It's not a watertight argument, but until someone provides an alternative that achieves the same thing I think we will see people continuing to do string theory.
Personally I do like to look at the alternatives even if they do not succeed where string theory does. You have to understand the failures to know how to succeed. Loop Quantum Gravity does not work at a perturbative level but it provides some pointers about the kind of mathematics that applies to non-perturbative gravity and its origins are close to those of string theory. Its offshoots such as spin foams, group field theory, quantum graphity etc have some nice mathematics that may be clues about how to formulate string theory non-perturbatively. I find it more sad that people working on these things reject string theory than that string theorists reject the alternatives. Everybody seems to work in a very narrow band of ideas. Instead they need to stand back and take in the big picture, think about what works and what does not work in different approaches, then consider how lessons learnt can be brought together.