This question is primarily discussing maths education for adult learners, on courses teaching engineering mathematics at an undergraduate level. These students generally never set out specifically to learn mathematics, but need to in order to obtain necessary qualifications for their career.
I frequently find that students arrive in my classes with unfortunate preconceptions about mathematics. In particular "I was never good at maths", "Maths is too complex for me" or "I just don't understand maths". This notion that mathematics is beyond the ken of mere mortals seems to be a widely accepted cultural phenomenon (How would a movie show the audience that this scientist is a genius? By showing them working on a blackboard filled with impenetrable equations). I've had onlookers walk past my office, and remark how complex my whiteboard looks, when it's normally some simple calculus revision that I was going over with a student. I politely say that it's only complex to them because they haven't seen it before, but I always just get the "Well I was never good at maths" answer. I've even over-heard colleagues teaching more qualitative modules say these exact words to the students.
This preconception is often so pernicious that it is very damaging to their future prospects. Whenever such students are taught some particular method for dealing with a problem, (e.g. transforming an integrand into a different coordinate system) they see it as "this was a technique I never could have seen myself, and therefore this is too hard for me to learn", rather than "this is the technique that I need to familiarise myself with and learn when to apply". When they struggle with a problem, as everyone does from time to time, they see it as reinforcing that "they cannot do maths", rather than seeing it as something that can be overcome through practice and effort.
Although many academic subjects have this problem, I feel that maths suffers from this "mystique" issue more than most. Are there any teaching strategies that are good at trying to break down the "I just can't do maths" barrier?
EDIT: Some comments are raising the issue of "what if the student actually can't do the maths"? This is a complex secondary issue with a lot of history behind it, that I believe is beyond the scope of this question. I think it is manifestly true that there exist students who have the ability to learn the material, but mistakenly believe they cannot. This question is purely concerned with the best way of helping those students, and not on adjacent issues.