Yes, I think that this is related to the issue and is causing our problem, I have never noticed that code before. Now I need to figure out what is stopping ajax search from working properly, and then replacing 'post_type=product' with 'woof_parse_query=1'. If it's not woocommerce that's doing this, it might be a plugin that has recently updated.
Any ideas what would use 'woof_parse_query'? I am not asking for you to look into this (as it doesn't look like a problem with your plugin) but just if you have any ideas at all.