Balloons, by their very nature, are at the mercy of the wind, and can’t maneuver out of the way of other objects except by (very slowly) climbing or descending. For this reason, mid-air collisions are fairly common whenever and wherever large numbers of balloons occupy small volumes of airspace (especially because this inability to take evasive action essentially restricts most balloons to uncontrolled airspace, which, in most places, is a very small layer immediately above the ground); fortunately, as balloons are very slow1 and very soft, balloon-balloon MACs are, generally, completely harmless (except in the extremely rare cases where a balloon rises into the basket of a balloon above it and gets its envelope ripped open).
Birds, on the other hand, are not necessarily at the mercy of the wind, are largely concentrated at the low altitudes where most balloons operate, are far more numerous than balloons (which is probably still the case even in the middle of a balloon gathering), and tend to come with a lot of inconsiderate pointy bits (beak, claws, probably other things too). Unlike with heavier-than-air aircraft, where a birdstrike usually just means a few dents, or, at worst, some unscheduled engine maintenance (although, as always, there are exceptions), a balloon could, if hit by a bird, easily suffer a catastrophic envelope rupture, followed quickly by (at best) a hard forced landing, or (at worst) rapid unscheduled lithobraking.2
How do balloons and birds avoid each other?
1: Not necessarily slow relative to the ground, but definitely slow relative to each other (since they’re being pushed by the same, or mostly the same, wind), which is what counts in a MAC.
2: Like the chapter in The Twenty-One Balloons where the protagonist’s houseballoon is punctured by a seagull, and he has to make a forced landing on a beach.