Reflexes
When it comes to physical reflexes, they are for the most part fixed.
The link provided involves exploring a knee-reaction due to hitting the patellar tendon...
"Okay, so I hit, and what happens is... her leg kicks forward. There’s a muscle contraction happening..."
This reflex is due to a sensory neuron connected to a motor neruon, but doesn't involve mental processing.
Learned Responses
Certain other behaviors that were learned over time, and have become "automatic", might be difficult to change, but might be able to. Sometimes, they can be over-ridden by "learning" a different reaction (using similar scenarios). So for example, one might have an involuntary gag-reflex when they consume certain vegetables, but over time, lose sensitivity to those things.
Thoughts
Although you asked about actions, there may be evidence that we can over time change both "automatic" actions and thoughts. "Automatic" is in quotes here because typically these are behaviors/thoughts that our brains have been trained to perform over a long period of time, and practiced so much that we basically due them by default, and one might argue involuntarily.
Research indicates that many people have subconscious racism, but
"habit-breaking intervention allowed individuals to overcome implicit
racial bias"
Since our brains control actions through the motor-cortex, theoretically, there are some actions too which, if the associated neurons pass through your motor-cortex, then by constantly practicing and training your body through mimicking the situation, you may be able to consciously override the default reaction (more easily over time).
