Non-correlation does not imply independence, that is, if two features are not correlated (i.e. zero correlation), it does not mean that they are independent. But (non-zero) correlation implies dependence (see https://stats.stackexchange.com/q/113417/82135 for more details). So, if you have non-zero correlation between two features, it means they are dependent. If they are dependent, then one feature gives you information about the other and vice-versa: in a certain way, one of the two is, at least partially, redundant.
Unnecessary features might not affect the performance (e.g. the accuracy) of a model. However, if you reduce the number of features, the learning process might actually be faster.
You may want to try some dimensionality reduction technique, in order to reduce the number of features.