2. New York City FC
A lot of fans of both clubs hate this being labled as a rivalry, but I think they have it backwards. It's hard to manufacture memorable moments between two teams, and these two have had legendary games. I'd go as far as to say the three biggest games in Orlando City history all came against the Pigeons: the first MLS game, the opener for Exploria Stadium and the playoff win*. There's a reason an NYCFC player isn't even in the picture I used for this section.
I get that this rivalry is a bit one sided in legendary moments, but there's something here. I feel a genuine contempt for New York that I don't have for most MLS teams and most of that comes from the permament link with Orlando as expansion brothers (and a wee bit of anti-City Football Group to push it over the top). To me, this rivalry could and should be a huge deal for both fanbases, but it's not treated that way, at least not as much as it can be.
*I forgot about The Running of the Wall in the initial draft, so add yet another wild moment to this series.