I also think that you should advertise yourself as vegan, so you’ll attract clients closer to your philosophy. This doesn’t mean that you should not help or work with others who do not agree with your views (your choice of course). As a health coach you might not have to be to specific with nutritional information and or recommendations. You will need to check how far you can go with this certification.
Your job is to help others make better choices for themselves. This can be achieved by providing them with as much information as possible and then let them decide what works for them according to their needs, goals and preferences. Not always one size fits all.