A westernised Ming, currently, will have no problem converting, as long as they have one of the two religious idea groups. Converting same culture provinces with max pious is quite easy, even for china.
And the benefits of being Muslim is more than worth it.
I wish you at least need to waste some 1000 mil MP or bash a few religious revolts before getting that job done...
On the other hand, a broken China should be more interesting religiously. China had a few Muslim warlords during early 20th century actually...