Updated: Apr 15, 2020
This is a problem for many, especially if exercises classes never teach you "neutral spine".
Why is this a bad thing! Neutral spine with a strong core hold, provides excellent stability through the spine and is a safe working posture.
Riding a horse and especially allowing your horse to move freely and to his best ability require you to have a strong core that is stabilising and supporting your spine, in every position. We move into and out of many postures when riding and more so when also caring for our horses. When riding, your core must contribute and allow the movement pattern as well as stabilise the spine.
Applying aids through your seat requires your pelvis to move into different tilted and rotated positions, this is not "neutral spine". So if you start working away from neutral spine then you must know how to engage your core in every posture, not just "neutral spine". I think this is the movement that riders are finding difficult and hence are not transferring their core strength to applying aids in the saddle. Prior to applying aids, a rider must be able to ride the different paces applying effective stability for maintaining good posture.
To be able to ride well you must be able to use your strong core in movement patterns that are specific to the riding patterns. Training your core to stabilise your posture while you train specific rider movement patterns will teach you how to transfer your core strength to your riding but at the same time be an allowing supple rider.