One, it matters to the extent that incorrectness interferes with communication and only to that extent. It is important to distinguish between incorrectness which impedes successful communication and incorrectness which doesn't. Mistakes that matter from a functional point of view and mistakes that don't. Correctness also matters more in some cultures than in others from a point of view of acceptability. If I speak a foreign language very accurately, I may have more chance of being accepted by a community that speaks that language than if I speak it with a strong foreign accent and make a lot of mistakes.
Cultures vary greatly their attitude and their acceptation of difference.
You might do very well speaking rather incorrect English in California and less well in Hampshire. Teachers, examiners and potential employers have enormous importance here. If employers decide that they are only going to consider applications that are written in perfect English, then people are going to have to learn to avoid mistakes. They will have to spend all their time doing that instead of doing more useful things with their time and this is the case in quite a lot of contexts. There is a psychological type which is common in the teaching profession.