A recommendation is not a prescription. Yes, a condo can have by-laws that prevent you from having pets. You could attempt to bring a Civil Rights suit, but I don't believe it would be successful.
You can approach your board with a petition for exception. Ask the board to clarify its position on pets, so that you understand what parameters you will be required to meet with your petition.
Read your governing documents so that you understand the petition process. Bring the medical recommendation and proof that the animal is well-behaved, up-to-date medically, and small enough for you to carry.
Communities, especially hi-rise communities, ban dogs, because of the inability of some animals to behave in a consistent, calm and civil manner in common hallways and elevators, thus disrupting and disturbing other people.
