I don't say that a horse is "disrespectful". I think that attributes to the horse a negative intent that is too human. Horses are pushy, in my experience, because they've been taught to be that way by their human handlers, often without the handlers intending this. This is regardless of whether a horse is naturally a dominant personality with other horses, or not. Horses are completely capable, in my opinion, of distinguishing people from horses and treating their human handlers in the ways that their handlers define, regardless of herd status. I think the most important thing to remember is that if you don't establish boundaries, or tell your horse what you want him to do, he'll make the decisions and they may not be ones you like. It's just a matter of knowing what you want and communicating that clearly to the horse.
There are a couple of different situations in which pushiness tends to come up: leading, feeding food or treats and crabbiness. Leading is a problem for many people - there are a lot of horses out there who walk all over their owners, but it's not the horse's problem, it's the owner's. Many people feed their horses treats, and the horses become pushy, or the owners worry that if they feed their horses treats that they will become pushy or nippy. Some horses get pushy when fed hay or grain. Some horses are crabby - particularly mares - but also some geldings - and will bite or make ugly faces when groomed, tacked or handled. This is often a combination of physical problems and training issues, and it's important to distinguish between the two things.
I think dealing with these issues is a matter of: being clear in your own mind about exactly what behavior you do want (notice I didn't say what behavior you don't want), communicating that as clearly as you can to the horse, being consistent and fair with the horse ("wait - yesterday I asked and you said that behavior was OK, but today it's not? what do you want?" the horse says), and rewarding the behavior you want. All of these issues are really about defining your personal space so the horse understands that you have boundaries and will abide by them. So here's what I do with my horses in a couple of circumstances - with a couple of stories thrown in:
Leading. I believe in being safe when I lead, and this requires that I establish boundaries for my personal space and make sure that the horse understands what they are. Consistency is really important here - if you don't want your horse to dive for grass when you're leading, don't let the horse do it, even once - otherwise they'll always be hoping there's one more time. When my horses are wearing their halters, they're working and grazing isn't part of the program. My definition of personal space is an arm's-length - the horse is supposed to stay outside that boundary at all times unless I move inside the boundary. Remember - if the horse "asks" if it's OK to bump into you by doing it, and you don't say anything, you've just given the horse a "yes" to the unwanted behavior. The more consistent you can be - this requires close attention, all the time, especially if you're trying to establish a new behavior pattern, and yes that's tiring - the better your horse will understand what you want and be able to comply. If you're inconsistent, and sometimes allow a behavior and sometimes not, that's not fair to the horse, and is a great way to teach the horse to ignore you. Be aware, all the time when you're interacting with a horse, in the stall, when leading and on cross-ties, or whatever you're doing with the horse - every interaction counts - of what the horse is asking and what your (maybe unintentional) answer is. Here are a couple of older posts that contain a lot about what I do when leading:
Treats and Feeding. In my mind, these two things are related - they're both about food and the uses of food. Most horses really care about food, and some horses care even more than others. When feeding hay or grain, if I'm going in the stall, I expect the horse to step back away from the food before I give it, every time. Since I'm consistent, the horses automatically step back as soon as I open the stall door - even the horses who are greedy. Same rules if the horse is in a paddock. If a horse acts up at feeding time - kicking, body-slamming or running teeth up and down the wall - I've learned that sometimes this isn't bad behavior but rather indicates pain from ulcers. Sometimes horses with bad ulcers can become dangerously aggressive when fed, due to the pain, but sometimes serious aggression can be due to other causes.
Same deal on treats. I don't have a strict rule against feeding treats, because sometimes they're useful in training situations, whether you're using clicker or not. Whenever I feed treats, I have rules about how the horse is supposed to act, and I consistently enforce them. Before I feed the treat, I ask the horse to back up a step or two, and then I move to the horse and feed the treat. The horse doesn't come to me, or mug me. I move into the horse's space, the horse doesn't get to choose to move into mine. If your horse is mouthy, it's because he's "asked" and sometimes been told that's OK.
Crabbiness. I think it's important to distinguish between different causes here - some horses are crabby because they hurt and some because they want to express an opinion. Horses can be crabby for grooming, tacking or handling because they hurt - this can be due to ulcers, chiropractic issues relating to muscles or joints, saddle fit issues - the saddle hurts once they're ridden and they're anticipating that, or bit/dental issues that make the bridle uncomfortable or painful. If a horse hurts, it will tell you so, and it's important to listen. Once these things are ruled out, then a horse may be crabby if it's a mare due to heat cycles - some mares experience back pain during their cycles. If this is extreme, it may be necessary to explore some alternatives, like supplements, that may help - I use Mare Magic for my mare Dawn and so far we've had good results. I don't tolerate crabby behavior, although I try to rule out physical issues first. If it isn't a physical issue, it may just be a habit - then there's the old "pointed finger just happening to run into the side of the muzzle" trick - if you can make them think they did it to themselves that may be just the trick to stop nipping. Some horses respond better to reassurance and praise - you need to know the horse and use the appropriate technique.
Jen - hope that gives you some idea of what works for me!