No, it is not considered normal or appropriate for a therapist to engage in "touchy-feely" behavior with their clients. The therapeutic relationship should be professional, ethical, and boundaried. Touching or any form of physical contact beyond a handshake is generally not a part of standard therapy practices.
Therapists are trained to establish and maintain appropriate boundaries to ensure the safety and well-being of their clients. Touching can be misconstrued, lead to discomfort, or even be harmful in a therapeutic context. Physical touch can trigger various reactions in clients, and therapists should respect personal boundaries to create a safe and comfortable environment for the therapeutic work.
Ethical guidelines and professional standards of most mental health organizations and licensing boards explicitly discourage therapists from engaging in touch beyond non-intrusive gestures like a handshake or an occasional pat on the back if culturally appropriate and agreed upon in the therapeutic relationship.
If a client ever feels uncomfortable with a therapist's behavior, including any touchy-feely actions, they have the right to address their concerns and discuss them openly with the therapist or seek support from a different professional if needed. If a client believes that their therapist's actions are unethical or inappropriate, they can report the behavior to the therapist's licensing board or relevant professional association.