I am not an overall Asia expert, but have traveled extensively to Thailand including several trips in September. I would not necessarily rule it out as a destination.

In my experience, the rain is mostly an afternoon event of short duration. There have been one or two times with a longer significant rain event, but it was not very disruptive to me. I actually enjoy watching the big rains, usually ducking into a bar to enjoy a drink along with the view.

Perhaps it is because I am a frequent visitor, but I don't let the possibility of rain detour my plans. It is just part of the landscape to appreciate.