I'm not so sure. Yes, Erdo and Bam were best Muslim buds. And, their policies in Syria have clashed. But, they both want Islam to spread and thrive. The falling out may be more over egos and tactics.
Erdogan sees himself as the Sunni caliph, right now, and wants to expand Turkey into some of the former Ottoman provinces. Obama may have a grander vision of himself as some sort of Mahdi--he's bringing Islam to the US, to Europe, and Syria is the means.
You are correct. I should have stated that differently. Erdogan lost the USA when his pal Obama was defeated and Trump was elected President. I am sure they are still the best of friends.