When the best time of year is to visit Mahale and the chimps depends to a degree on what your objectives are.
If your primary concern is to see the chimps, then while the obvious time to be there is during the dry season (June to October), there are good reasons for thinking about visiting Mahale in the low season, which means the time between November to March.
The season is low because it doesn’t suit humans quite as well as the high season. The same isn’t true of the chimps who don’t give a fig about the weather. The bonus about going at this time of year is that it costs less, and there are far fewer people there. But having spent many months in Mahale during the rains, we can testify to it still being a superb experience for the chimps (and a lot else besides).
If on the other hand, you like the idea of more predictable weather and all the things that go with that, then it is worth paying the extra cost of going during the dry season – June – October.