ETA: this got pretty long and off topic, but I mostly suggested therapeutic riding because OP seems to be looking to combine the passion for horses with some kind of vocation or sense of purpose which this does for a lot of people. It’s not for everyone, it just depends on what you’re looking for.
As with everything else in the horse world, quality can vary depending on the program, and there’s nothing stopping anyone from hanging out their shingle for “therapeutic riding” with no qualifications whatsoever. That said, most of the certified programs I’ve been around have had very high standards of horsemanship - they may not be your standards, and there are things that make sense for that type of program that wouldn’t work elsewhere, but providing quality care and training is essential as a safety issue and for maintaining the longevity of the horses. Many of these programs see a large volume of clients and volunteers every week. The priority is always going to be on doing things safely and consistently, and streamlining things where possible because time and labor are limited. That means some of the “nice to haves” that aren’t safety or welfare issues may not be as high priority as they would in a private barn - it’s just the reality of trying to keep a program like this running. This is prime “don’t let perfect be the enemy of the good” territory.
How long did you actually work with this program? It doesn’t sound like you were there very long, and initial training is usually focused more on getting people up to speed to support lessons, not so much on the horsemanship side, since that’s the main need for volunteers and frankly a lot of volunteers don’t stick around long enough to make it worth figuring out if their claimed experience is legit or not. You do have to prove yourself a bit first, and they still have to confirm all your basics before moving on to areas where you can actually learn something, so it can take time. The primary focus will always be on supporting clients and horses; volunteer enrichment will always take a back seat to those goals, but was absolutely on our list of priorities. Education was something free and easy we could do to show volunteers how much we valued them and help them get as much out of the experience as possible.
Honestly, your post is kind of why it was often easier to get volunteers with no horse experience at all. A lot of horse people came in with very strong opinions on How Things Should Be Done (which of course all contradict each other!) and often jumped to judgment instead of trying to understand why things that work in a show barn might not be ideal for a therapy program. I always made a point to explain why we did things the way we did instead of just telling people the policy so they could learn. Usually there were very good reasons that weren’t obvious to people new to the program, but sometimes the reason was just that when you have that many people coming and going every week, at some point you have to just pick one way out of the multiple “right” ways and ask everyone to adhere to it to keep things safe and organized.
This is definitely not true. The vast majority of therapeutic riding instructors that I’ve known are people who have deep horsey backgrounds and wanted a job in the industry that wasn’t going pro. There are others who come into it from the therapy angle but they’re the minority, and in any case just going through the PATH certification process will get a person a good amount of horse experience. Either the more horsey instructors will handle the more advanced care and training, or larger programs will have a dedicated barn manager type on staff as well.
Not every instructor needs to have deep horse expertise, and it’s helpful to have a variety of strengths on staff since these programs need such a wide range of skills to function. You’ll also typically see some instructors with more of a non-profit/fundraising background too. These programs don’t have the budget for large staffs so everyone wears multiple hats, usually teaching plus something more specialized.
Not that unusual for initial training to be done by another volunteer that may not be an expert. If you were totally new to the program they weren’t looking to you for horse experience anyway, they just needed someone to show you where to find everything and explain the basic routine. If she could correctly identify all the horses and complete basic grooming and tacking, she was qualified to show you how to do the same.
As an experienced staff member, it wouldn’t have been a good use of my time to show you around at first when someone else could do that while I dealt with the more complicated tasks on my list. I would have checked in with you a few times and asked trusted volunteers what they thought of you after your first few shifts, and then I would have started spending more time with you once you had the lay of the land and I could actually start to figure out how much experience you really had. I would have loved to do all the initial training myself but there was always more to do than time in the day to do it, so it just didn’t always work out that way.
This is a non-issue. A 17" saddle should be just fine for all but the tiniest of 6 year olds, and fit for the horse is much more important than fit for the rider. These lessons mostly take place at the walk and usually there are volunteers walking alongside, and proper equitation is not the main goal. The horses, on the other hand, work hard and carry a lot of unbalanced riders so their comfort is most important. The horse may have been hard to fit or had back issues that required a specific set up, or maybe the rider had physical challenges which made that particular saddle work well. Saddle fit is too complicated to involve volunteers who may not have all the relevant information or experience. Remember also these are nonprofits - they don’t have the budget to be super picky with big ticket items like saddles and often rely on donations, so if it fits the horse correctly they’ll try to make it work if at all possible.
It’s very common for each horse to have specific tack assigned to it that volunteers are not supposed to change without consulting an instructor. YOU may feel qualified to make adjustments, but so do a lot of people that really shouldn’t be messing with what’s been fitted by the program - if every volunteer starts swapping stuff out as they see fit suddenly you have a chaotic tack room and a high likelihood of a tack malfunction that puts a rider at risk. Maybe the horse was going through some weight changes, maybe he preferred that girth for other reasons and they were making it work until they could get a new size, who knows. Instructors check tack and girths before riders mount, so if it was really a safety issue it would have been fixed. We had so many processes in place to make sure everything that needed to be was checked by someone experienced, just because you weren’t involved doesn’t mean it wasn’t happening.
Same with the reins. For a volunteer used to the therapeutic program, the idea of taking apart a horse’s bridle would give them pause - and it should! It’s really not a huge deal, and if you hadn’t been there the instructor would have easily made the swap themselves. All it took was a 30 second explanation and now that volunteer can handle this issue herself next time.
You get a wide variety of horses in a therapy program, and not every volunteer is going to be equipped to handle every horse. The main program I worked with typically needed 200-300 volunteers on schedule every week - try finding 300 legitimately experienced horse people who are willing to donate their time regularly, it’s not easy! Most programs will separate out horses by difficulty level, and the staff do a LOT of groundwork as well, but honestly a horse that dives for the grass but otherwise isn’t going anywhere would not be a huge concern for me. The volunteer will either figure out how to assert herself or someone else will come yank his head up, it’ll be fine.
Honestly it doesn’t sound like you were involved long enough to find out, and may not have come across as that willing to learn considering how many things you considered them to be doing wrong right away. It’s not something that happens in the first few weeks or even months of working there, and if you go in just hoping to get something out of it for yourself you’re going to be disappointed, but you’d be surprised how much they’ll bring you in on once you prove you’re a team player.