First of all, some people's eyes already glaze over when looking at C. It's only accepted because it has become near ubiquitous in computing, and notation is much more palatable when it is consistent for a whole domain. This is a very important point that many people miss: the reason why Java, C#, JS, even C++ to some extent get away with lots of non-maths operators is exactly because they have chosen to copy each other. That's a very powerful thing.

Second of all, even within C, these operators are ubiquitous. You will use . and -> and * to deref and & to take the address, and = for assignment, and ++ or -- for increment/decrement, and ==, &&, ||, ! for logical operators, and the <operator>= notation for applying a change to a variable, and [] for subscripting, in almost every program you right in C. Shortening a very common operation to a symbol is much more easily acceptable than shortening a more rarely used operation, or one that's specific to a library.

Basically, the status quo in programming as I see it is this: it's OK to use symbols instead of words for (a) syntax in your language (C curly braces, dots), or (b) ubiquitous constructs that are used virtually all over any program (+=, *), or (c) if they are already well-known symbols in other popular languages, or in non-programming fields (such as the near-universal regex syntax). Even (a) and (b) benefit a whole lot from familiarity with other languages, as should be expected. They also still require proper names - which the C standard for example gives for every operator, as do C tutorials.