Please make the easy switch to having two teams be each others rival instead of having it be a random mixup. When one team has two or three teams gunning for them as a 'rival' and another doesn't have to worry about any added heat from any team it creates an unfair advantage that has nothing to do with the game. Rivalries aren't real unless both teams have added pressure to compete against one another...
Just sayin...
There are few more things related to this topic I think needs to be considered;
1) Should the amount of rivalries be purely random?
I'm not sure. Ususally, the richer teams and those that had enough reputation at a league will get more rivals along the seasons.
I think this should also be the case here.
2) Should the rivalries identity be purely random?
Again - I think it should not.
In this case, I believe that teams that "knows" each other more, are more likely to be rivals.
3) Should rivalry be a bi-directional thing?
Of course it should.
I don't know a team who their fans finds another team as their rival, but not the other way around.
4) It was said that currently there can be 0, 1 or 2 rivalries altogether.
But it is not exactly representing the whole story.
Currently each team can have 0, 2 or 4 games where the other team will try harder (and maybe will have higher audience influence).
Why not defining the rivalry to be from the second conference?
By that, it will at least have less affect.
REMARK - I have only one rivalry this season.