Well, apparently one DOES have to have a church in the game to get married so you have at least one priest. Although, can you have both churches in your game or just one, and which church seems to be better? I wish you could get married and be agnostic, lol personally, I hate organized religion.

Glitchie

You don't need to have a church in your kingdom to get married. The option should still appear to ask for hand in marriage, and then the 'have marriage' option should have, 'have marriage here' available with both the church options greyed out.
'Sky Priest' should still come down regardless of what buildings you do or don't have.

Weird. I ask because both times I've tried, it says the wedding was cancelled and asked if someone got cold feet. I tried with my knight or spy, can't remember which, and my monarch.

Aw, we've all had that I think. It's an annoying route fail. Sometimes what is blocking your way is not obvious, sometimes it's an object they won't walk round that they will every other time, and sometimes it's just people in the way. They barely give it a chance and then they cancel. Don't think Simmies really want to get married lol.
It can take quite a few goes to get them to stand together and wait. Try a different placement for the 2 of them, or if it's not overly important to you, a different location, although you shouldn't have to.
I find if I let the non-controlled sim walk away about 4 or 5 steps and then select again, it has a better chance of working than trying to catch them before they can move away.
One of the times it will take, just got to keep trying. It's really annoying I know, but on the brightside, your sims can remain agnostic like you want :D

If the location is not too important to you for a picture or something, try going outside. I have found that one main cause of this is objects in the way and outside you do not have that.