Personal Trainers are a very inclusive bunch, we're equal opportunity torturers. There are a few times that we have to turn people away, though, and they're usually health related. Personally, when I see someone who has made the effort to see me and I have to tell them they can't exercise, it's the worst part of my job. I know how much courage it often takes to make that first step so to thwart a person's effort is miserable for us both.
This refusal to see clients comes down to experience, safety and insurance. Advanced Personal Trainers like me can see clients with conditions that many others aren't insured to. Similarly, PT's with specific qualifications such as exercise for lower back pain or postural stability will be able to take on a wider client range. Here are a few conditions that often need the say so of both a medical practitioner and a PT with specific training such as an exercise referral qualification before you can embark on a new fitness program:
Coronary Obstructive Pulmonary Disorder
High Blood Pressure
Similarly, any heart related surgeries call for an additional level of permission before PT's are insured to work with their clients and best practice is to arrive with a letter of permission from a GP or consultant.
In addition, there are some conditions where a degree of experience and good links with physios are beneficial. If you have osteoporosis, osteoarthritis or are recovering from joint replacement surgery, I would recommend seeking a PT who has experience of these conditions and strong links to Physiotherapy units. They will know when is best to refer and will have no qualms about sending you back for your safety. A PT who knows when to stop training you is a PT you can trust.
In short, a PT who refuses you for your own safety is a PT you want. They're experienced and confident enough to understand their limitations. If in doubt, ask your GP before seeking a PT's help. Once you get their go ahead, we can get you moving.
Enjoy Good Health!