OP, having had mustangs for several years now, and for three of those years I boarded, I can somewhat answer your question. If the mustang is already saddle broke, it is typically already “fence broke” (i.e., does not need 6’ fencing to keep them in), and should be relatively easy to handle. If the horse is green, or still slightly squirrely on the ground, just be up front…the horse is green, like any other horse.
I brought in several BARELY TIP trained mustangs to the facility I boarded at over those three years. We did have some turnout issues with two of them, they were NOT accepting of new horses coming and going, so I ended up renting a back pasture that was just for my horses, so I could control who was turned out with whom. Other than that, I was honest about their training ( or in this case, lack of training ) and I was the only one to handle the horse. This was a self care barn, so it worked out well for all. One problem is multiple people handling a green mustang, or any green horse for that matter. It is imperative to be consistent in your handling and training of them, like any domestic horse, no matter who is handling them.
I have never run across any bias towards them, although I have had to correct a lot of misinformation. A lot of people found it really neat to discuss my mustangs, and a lot of the boarders asked if they could watch my training sessions with them (in the round pen, barnyard, etc). They thoroughly enjoyed it, and said they learned a lot in the process.
I think the only instance you would have trouble in is if you are adopting straight from the BLM, unhandled. In that case you would need to find a facility with the proper set up…6’ fences, with a shelter. In that case you could find a local TIP trainer near you that has the proper facilities.
However, since you are planning on adopting an already saddle broke mustang, it shouldn’t be much different than a domestic horse. Good luck OP! Mustangs are wonderful horses. I have only run across one that didn’t settle into domesticated life well (and she was older…in the pens until she was 9 and was still unhandled). They have taught me more than any domestic horse I have ever owned, and have seriously improved my skills. They can make truly amazing partners.