It may be rain this evening = It may rain this evening. It might be raining this evening. = It might rain this evening. Cheerios, have a good one!

Neither one is correct. "It may" is what people say when they mean "it might". To my mind, though, it's not a great idea to mix up "may" and "might" because they mean different things and one day you might need to use one of the words to mean what it actually means. "May" is about permission; "might" is about probability. In this sense, I mean. They have completely different meanings, too (like a month, and strength, respectively). Anyway, if you want to say that there is a non-zero probability that it will rain this evening then my advice is to say "It might rain this evening".