Is david tennant allergic to animals?

Answer 1

No, otherwise in the episode Gridlock he would have a rash or sneeze from picking up Captain Branagins kittens.

David Tennant is however very allergic to horses. He had to take allergy medication when he shot Casanova, and the Doctor Who episodes Girl in the Fireplace and The End of Time (there were no horses in The End of Time but one scene was shot in an empty stable and his allergy is bad enough that simply being in a room where horses had been meant he had to take medication). He talks about it in the commentary for The End of Time.