Speaking as another bread-baker and former baker I'll say this...gluten is highly important to give bread any kind of leavening. As everyone knows, yeast is what causes bread to rise, through it's multiplication which gives off amounts of carbon dioxide gas. Without gluten, the carbon dioxide is able to rise through the bread and far less is trapped, resulting in flat breads.
Not always a bad thing. Tortillas, pitas and lavash are all made with unleavened or lightly leavened breads, but they're not what most people would consider a 'loaf' of bread.
Take a look at the different types of wheat we have open to us. The most common designations are hard winter red, hard spring red, soft winter red, hard winter white, soft spring white and durum. For the most part, we can divide the wheat used in breads into simply 'hard' and 'soft,' though.
Hard wheat flours have a protein content between 10-14%, with the highest protein going to hard spring red wheat. These wheats are considered bread wheats, and when you buy 'bread flour' from the store it was likely milled from these, with all-purpose flour made up of some of the lower-protein strains.
Soft wheat has a lower protein content, often below 9%, and it's flour is used to bake cakes and pastries. Cakes are leavened with chemical agents such as baking powder or baking soda, which produces more bang in a quicker time than yeast, which is a relatively slow-acting leavening process. You'll notice that cakes are still rather delicate. Anyone who has cooked them will tell you that the most frustrating thing is to have a cake 'fall' on you, which is when the contained carbon dioxide finds a way to escape and takes it, along with all the leavening of the cake.
Durum wheat actually has a higher protein content than either, but it's yellowish color makes it generally unappreciated for breads, other than certain Mediterranean breads. It's mostly used for pastas, and that's where the pasta you buy gets it's unique yellowish color.
As for wonder (wunder) bread and most major breads sold today. Strictly speaking, they're combination breads. They're often prepared with low-gluten flours, as low as 6-8%, and while they do have some yeast in them, they're also leavened with bicarbonate of sodium, or baking soda. The combination of the two, along with the low protein content and the over-processing of the grain causes the texture of the bread. You can tell it was done with chemical leavening because of the tiny air pockets inside of the bread, the same that you might find in a cake. Compare that to 'botique' breads that you'd find elsewhere, and you'll clearly see that 'real' bread generally has rather large holes in the crumb.
The original reason for the name 'wonder' bread, was because they could take a loaf of bread from raw flour to finished bread in under an hour and a half, which was a 'wonderful' thing. The very open crumb structure of the bread even lent itself to quick cooking, which meant that a softer crust was formed. Anyone who's cooked bread knows it takes about fifteen minutes of hand kneading (Or five in a mixer) plus an hour for the first rise. After that, it's another half-hour or so for the second rise once you punch it down, and about another 45 minutes to an hour for the bread to cook once it's risen a second time.
And yes, I know there are no-knead breads and breads that can be finished quicker. I've even experimented with them. In this case, I'm referring to the French-style baking that I was taught.
I was going to write in the way to cook 'real' bread here, not some monster hybrid bread like wonder bread, it'll blow peoples minds. Anyone interested can PM me. However...I think most of the people here know already. Which is a minority, let me assure you. Real bread has a crust to it because of the long baking period (relative to wonder bread, which is often done in as little as 20 minutes once it goes in the oven), the action of the yeast and the skin that forms on the bread because of the gluten. Real bread often has a more open crumb, unlike wonder bread, though there are some varieties that will have a fairly close crumb.
But most importantly, real bread has taste. A dip of olive oil or nothing at all is required to make bread taste good.
To get back to the original posters question...I've got about 80# of wheat put back in several buckets that I originally bought from the feed store for grinding to make bread. I made sure to get triple washed wheat and the 20 or so pounds I've already eaten have given me no ill effect. The key thing to look for is triple-washed.
Just my .02. Use or abuse as you see fit.