If a therapist had tattoos they would most likely hide them, as they give off a certain impression and even though that impression can be totally wrong, it's still the world we live in. Most organisations would insist in them being covered and anything other than ear piercings be removed. A therpist in private practice may use more leniancy but most clients would be put off.
I am in training to be a therapist and I have a tattoo but it is on my back and would never be seen by a client, so I know it wouldn't affect them or what they thought of me.

Many professions would ask someone with tattoos or piercings to cover or remove them during working hours so it's not just therapists.