I got challenged by the opponent to join Blake Steele's team and the opponent won't pop for me to fight it in the Coliseum. Hard refreshing and restarting browser haven't fixed it. It doesn't seem that fair that I'm kind of... sort of... really locked out of plot stuff because of this.

I had this problem for Team Steele as well; look under the 'Event' tab for Challenge An Opponent. Both team dummies are there.
it should show up under the 'event' tab on top
Oh.
That never popped either. O.o

If it doesn't show up for you, this link should do the trick.
Could you please describe, what happens when you join to one team?
When you click to apply, you'll have to fight that team's dummy (you only have to fight once). You can then join, or decide to check out the other team (to fight that side's dummy). Or, you can join.
Nothing else happens, since this is the only step so far.