For those that think the couple has the final say because both the officiant and photogs are there to provide a service, think again. There is a hierarchy at a Christian wedding and, surprise, the minister is at the top. They call it "preside" over a wedding because he is THE boss. And he was given that responsibility by the B&G. Look up the word if you don't believe me, "president" derives from it.
If they don't agree with the religious component of the wedding, they can hire an actor or JP or whatever. If they feel it's about the photos, maybe they should have gone that route.
From what I can tell, the video was set up either right on top of, or way too close to the altar (sanctuary). I have $5 that says the priest never approved that location ahead of time, regardless of his denomination.
The edited clip speaks volumes as well. It is trimmed to show the priest in the worst possible light, probably so that it would go viral (as it did). You can push someone's buttons all day until they blow up. Only post the outburst and voila, you get what we see here.
Bottom line: it's the officiant's show. They bought into his belief system, at least for the day. Fall into line and STFU. To complain about it is like voluntarily joining the army and then complaining about the stupid war you got sent to. Suck it up, buttercup.