The intestines (gut, interchangeable) are a weird place to imagine, and a harder place to study given the apparently 'unethical' way to cutting a human open after they eat just to poke around.
You can imagine the gut the best as a large muscular tube with round folds poking towards the center (without these folds, it would otherwise be cylindrical). In the small intestine are an assortment of receptors and transports that take up compounds, and plenty digestive enzymes to break down food stuffs.
Two concerns I want to outline with the small intestine and supplementation:
Things that inhibit enzymes are never 100%. Something like Green Tea that inhibits pancreatic lipase (the fat digestive enzyme) will not inhibit all of the fat from a meal from being taken up; its just not that powerful. It could potentially inhibit uptake of a few grams of fats if taken on an empty stomach, but nothing as grand as a meal. Worrying about green tea's lipase inhibition and not taking fat-soluble vitamins or compounds at the exact same time is a fairly moot point. There will be some fat uptake, and the vitamins will wait around in the lumen (inside of the gut) until they get a transport
Transports that share substrate, such as the divalent mineral transport that transports Calcium, Zinc, Magnesium, and Iron, can definitely be maxed out. However, as long as they stay under the max amount then there would be no inhibition. For this particular transport, the limit cap appears to be around 800mg. Taking Magnesium and Zinc with total levels below this amount should not cause either one to not be absorbed, since together they are still both under the limit cap.
Some of the 'do not take with' supplements are conditional, and one should read a bit of the compleat summary or use Ctrl + F to find the area where it will be discussed further.