I used to be a shadow for a personal trainer. Whenever he wasn't there to work I used to train his clients. Bsed on my experience, touching will most likely involved to correct posture and for spotting. If you are uncomfortable with that, there are many gyms where they have a diffrent aerobic classes. You can attend those as an alternative. Many of them actually work on building muscle as well and has female instructors. If you want my honest opinion though, if a personal trainer touches you, it's not because he's doing it for the sake of touching you, it's to help you. They are health instructors and fall along the lines of a doctor. When I trained some of my boss's clients, some were Muslim women, and before I started to work with them I clarified them about touching. Most of them were actually surprised that I knew about it, and after I explained it to them, they allowed it because they knew it was for health reasons.
If you are gonna have a trainer, their job is to make sure you don't hurt yurself and a lot of times to do this they will need to spott you which involves touching.