Satan can possess you if you open up that dialogue with him yourself. He does not freely just enter a body.
The physical practice of yoga is not satanic. The mantras, and slippery slope into transcendental meditation are what “opens up the doorways” and thus can lead to possession or unwanted spiritual occurrences.
Believe it or not, my mother in law did this. She’s not Catholic, but Protestant and had taken to going to a cemetery where some of her long deceased relatives are buried. She took photos of the headstones and as her Protestant church teaches, it was perfectly acceptable for her to ask spirits to “involve themselves” in her life and steer her towards God. When you do something as idiotic as that, it invites all spirits, whether good or bad, to latch onto you.
Flash foward about 3 months later, and she told me that she had to stop visiting the cemetery because she was afraid she had “brought something bad home”. Loud thuds, objects falling and moving. I personally witnessed a glass vase on a coffee table flip upside down in the air off the table, totally unprovoked without rational explanation.