The core and spine is crazy complex. For starters I've learned a whole bunch of new muscles: glute medius/max, QL, serratus, interior/exterior obliques, multifidus, upper/lower/transverse abs, inner thighs, quads, hamstrings, hip extensors/flexors, lats, spinal extensors/flexors, rhomboids, upper/lower traps, pecs minor/major, levator scapulae...
That sounds like I've just rattled off some anatomy but literally all of those network together to mobilise your spine and any one of those being out of whack can cause cascading and coupling issues of other nodes in the network.
Glute weakness for sure is one of them so could any of the other ones...