For most of mathematics, potential new entrants would be mathematicians from a different field. Then using familiar notation is actually helping them understand the new concepts, even if it erects a barrier for people with zero background knowledge. But if you have zero background, you'd be better off starting from the fundamentals (and learning the prevalent notation on the way) rather than diving straight into deeper mathematics.

In that, notation is really no different from a specialized language. A sentence like "a monad is a monoid in the category of endofunctors" doesn't make sense if you don't know what those strange words mean; but if you understand the concepts, you probably also know what they are called.