I found plenty of examples online:
The beef-averse have a good option in the Fish Sandwich ($3.99) with two planks of whitefish, tartar sauce and lettuce.
The whole thing is topped with lettuce, tomatoes and “special sauce,” and there's also a version with chicken fillets for the beef-averse.
Grilled “huge steaks” are the main attraction here, though the beef-averse will also find alternate bistro options.
Or you could simply say "beef abstainer" or "non-beef-eater". While searching I found several instances of "bovinarian" (beefeater) after the example of "pescatarian" (fish-eating vegetarian), so I guess "non-bovinarian" and perhaps "non-bovivore" are possibilities too. By the way, pork-eaters and lamb/mutton-eaters appear to be porcinarians and ovinarians respectively.