Doesn’t Stannis conventing to Rhollor invalidate his claim to the Iron Throne? Aegon was anointed in old town and one of the names of the King is Defender of the Faith- couldn’t Renly or another King claim they were defending the Seven here?

Not really, no. Aegon was anointed in Oldtown, but that wasn’t what made him king – being acclaimed by the lords of all of Westeros did that. Being anointed in Oldtown and dating his reign from that date was just good PR. 

As for the Defender of the Faith title, that’s the just the title that Jaehaerys adopted when he agreed to end making war on the Faith and they agreed to surrender their independence both judicial and military – it’s not a legal requirement. Indeed, prior to that, the Faith made war on the Kings on the Iron Throne – both Aenys I and Maegor, the former of whom was declared an abomination in the eyes of the Seven. And Jaehaerys and every King since has descended from Aegon the Conqueror through Aenys I, so if the Church was the arbiter of who got to be king, there’s a bit of a problem there. 

I think the problem people are having here is that they’re thinking of the Westerosi monarchy as like the Holy Roman Empire in the phase in which the Pope had to sign off on the HRE in order for the Emperor to be Emperor. And that’s not the case. It’s far more like the period in which the HRE got to name the Pope.