I think a lot of who you consider rivals is dependent on who the big games are against when you first properly start supporting Alty.
I know it's pretty much sacrilegious but I had always considered Northwich bigger rivals than Macc. Having never seen us play Macc they felt more like some mysterious boogeyman rather than an actual rival. However now Northwich are nothing (which is actually quite sad) I can see why Macc are now top of the pile.
After that I've always considered Southport and Barrow as decent rivals, both clubs with a similar history to our own and always bring decent support with them. The matches don't have the needle of derby matches but we've had some cracking games with both sides in the league and cup.
However, the weird thing is I don't actually have anything against either Southport and Barrow. I enjoy it when we beat them but I don't actively dislike them. There seems like there should be another category that aren't exactly rivals but you do really sort of despise them.
Into this category go Accrington Stanley - possibly the most wanky fans there are, so up themselves that they make FCUM look relatively modest. Tamworth - the games against them were always horrible, Heathcote didn't help things with his constant arguments with their fans in the shed but really quite a knobbish club. Kettering Town - massive ideas above their station, seem to think that because the town turns out when they're lop of the league they're sleeping giants.
However, I am willing to admit that my views on Accrington, Tamworth and Kettering might just be the result of paying too much attention to some knobs on the internet.