Your principles and beliefs really have little to do with this.
You say you are a “certified personal trainer.” Did you not ever learn to do anything new? Something new as your training was made up-to-date? And do it for the sake of your clients’ benefit if not your own? For the sake of others?
This change of habit is done for the sake of others, that’s all. These are people who have an understanding of their own gender, which is more fluid than your “old-fashioned” understanding and is reflected in their use of new pronouns. That’s all. You show respect for that new understanding by learning to use their pronouns as they use them, not as you used to use them, the “old-fashioned” way. Isn’t that simple?
Do your principles and beliefs not allow you to do things for the benefit of others?