as a coach or trainer, we should give the advice that is best for the client regardless of which limitation we choose to pose upon ourselves.
I am a vegetarian myself but when I talk about protein options with clients, of course I include all possible protein sources, including those coming from animals.
By your definition, would you advise a client against riding a bicycle just because you don’t do it yourself? Of course not.
I believe that you cannot be a good coach / trainer when you impose your own prejudices on others.