While it is true that according to Einstein's theory of general relativity, in a state of freefall, a person would not feel the downward acceleration due to gravity, there are factors at play that can cause sensations during skydiving.
When skydivers jump out of a plane, they initially experience a sensation of "dropping" or feeling their stomachs "fall." This sensation is primarily attributed to the sudden change in velocity and the resulting forces acting on their bodies. As the skydiver accelerates downwards, their body is subject to an upward force from air resistance, which opposes their motion. Initially, when the skydiver jumps out of the plane, they have a high velocity relative to the surrounding air. The sudden deceleration due to air resistance causes a sensation similar to the feeling of "dropping."
Once the skydiver reaches terminal velocity, which is the constant velocity at which the force of air resistance equals the force of gravity, the sensation of dropping diminishes. At this point, the skydiver is in a state of freefall, experiencing zero net force, and thus would not feel any acceleration or force related to gravity.
If you were to freefall on the Moon with no air resistance, the experience would be different due to the absence of significant atmosphere. Without air resistance, there would be no sensation of "dropping" or feeling the stomach drop as there would be no resistance to oppose the motion. You would feel weightless during the entire freefall, similar to the experience of being in a vacuum.