Thought I'd weigh in here.
Years ago, my mother bought herself a nice neoprene cinch, because she thought it looked like it would be more comfortable to the horse. Nice and wide and padded and soft.
I started using her horse and saddle for some pack trips while I was in college and couldn't keep a horse and gear. Found the neoprene almost always left galls on the armpits of the horse during a long trip. Went back to string cinchas (mohair) and never had the problem again.
Neoprene is great for eventing or an afternoon of easy trails, but for putting mileage on a horse they just don't do well. Most people buy them (like my mom) because they look soft and cushy. Fact is, they don't breathe, they hold heat, cause the horse to sweat, then the sweat against the neoprene causes rubs and galls. I've had the same experience with the heavy felt cinchas.
A mohair string cinch breathes, sheds water, dries quickly, does not hold heat against the horse. Yes, they stretch a little when new, but not so much after they've had a few miles put on them. I've never noticed any trouble from the stretching. I tend to ride with a loose cinch anyway, but every time I take a break I loosen the cinch, then re-tighten it before I re-mount.
One caveat for string cinchas - for long rides, stay away from the wide "roper" cinchas. They can rub under the armpits on some horses, particularly with a full or 7/8 rigging. They also often have leather keepers in the middle that can cause galling after getting wet and drying a few times. The straight cinchas are better for long trails. This is one thing where cheaper is actually better!
I have observed that a lot of folks ride with too tight a cinch, and it makes horses "cinchy". If your saddle fits and you don't use too much pad, and you are a balanced rider...and your horse has withers...you really don't need the cinch very tight. If you can't mount the horse without your saddle turning, you might need to adjust your mounting technique.
I once had a mustang that was so barrel-chested that I had to use a breeching (butt strap) on him when I took him into the mountains. Before I learned that lesson, I was coming down a sidehill once and the saddle slid right over his withers and up onto his neck. Lucky for me he was a pretty calm horse. Could've pitched me right over his head and down the hill!