So if you assume that Logan is meant to follow after X-Men: Days of Future Past, then the future still doesn’t look good.
However, if you’d rather consider Logan a one-off tale set in a separate universe, then things will eventually become better for mutants, or at least the ones under Professor X’s care.
Of course, let’s not forget that Logan, which takes place in 2029, revealed that no new mutants had been born in the last 25 years, and the X-Men were no more after Professor X suffered a seizure that unleashed a destructive telepathic wave, killing several mutants.