I don't use the tub for a very different reason - mine is newer and acrylic and doggie claws could scratch that surface, especially if you had a dog frantically trying to climb out. This is not an issue with older enamel tubs. I am positive that with proper cleaning there is no reason your tub couldn't be as sanitary after a doggie bath than after a human bath. Tubs are not made of porous materials and are easily cleaned disinfected.
Our sheltie gets a bath in my shower which is tile and has an extra flex hose I put in just for that purpose.