Nope! There's myths about hypnosis that it can make people do things that they normally wouldn't do. And stage hypnotists know the truth about this, though they pretend for show that they don't. First off stage hypnotists take volunteers from the audience, which means most of the people volunteering likely want to be on stage doing silly things. Then the hypnotist asks them questions and does a series of suggestibility tests to see who is actually responding to their hypnosis. Spoiler; suggestibility is flexible! Even the most naturally suggestible people can decide not to respond to a suggestion they don't like, or decide not to be suggestible at all to a certain person or situation, and even the least naturally suggestible people can decide to let in certain suggestions or become more suggestible for a certain situation. And everyone, regardless of how suggestible they are, will (almost always) refuse suggestions that go against their values, feelings, or beliefs, especially when in trance (the state of relaxation we use in hypnosis). The exception to this rule is people who go against their own beliefs and instincts to please others when in day-to-day life. People with this protective strategy will sometimes try to please the hypnotherapist by following a suggestion that doesn't feel true to them, though they are more likely to follow their own instincts, feelings, and values when in trance, because it is easier for them to get in touch with their true feelings about things and have the flexibility of mind to follow them. Partly because of this but mostly because the suggestions are much more powerful and personal, I get most of my suggestions and all of my anchors directly from the client, using their own words.
tldr; Everyone is some level of suggestible, and it doesn't matter how suggestible you are naturally for hypnotherapy to work, because it is up to you how much suggestion you want to accept. People are more likely to follow their heart and gut while in trance, and very unlikely to accept anything that they don't want to. I will only ever anchor things that come from you, the client, directly, so all the take-aways from the session will be in your own words and hence very true to you personally.