Genetically Engineered organisms are in much of the food we eat today so it is immpossible to not be exposed anymore, and much of our food has been sprayed with all kinds of stuff that is not good to ingest and washing off simply moves it into our water supply so even if we do not eat them we drink them. Composting those materials does dilute them, somewhat, but you do what you can do to limit your exposure.
Even the most pristine organic garden will be exposed to contaimination, from the air and rain, and since we cannot control that we cannot worry about it.

Compost has been called the 'great neutralizer' because the decomposition process is able to take a variety of materials, some even harmful, and break then down into their harmless elemental components.

You do not necessarily have to limit compost to only "organic" ingredients to arrive at a suitably organic product. But you do have to have a first rate, active composting operation that achieves and maintains proper temperatures for a suitable length of time. That is the only way to be sure all the organisms responsible for the complexities of decomposition are doing their job thoroughly.

The definition of 'organic' has many interpretations. Under its most literal definition, compost by nature is organic - it is sourced from once living materials. That is most likely why you won't find much detail on creating "organic" compost :-) But if your composting process is thorough and achieves and maintains proper temperatures, there is minimal risk of persistence or contamination by less than perfectly natural materials that may be included, like GMO seeds, pesticides, medicines, etc.

The problem I see is that: 1) if you had oil or gasoline on oak leaves, which you composted. You could have the compost tested for the chemical of the oil or gasoline.
2) But I am not sure how you would know if the plant material was GMO or not. Even if you could, not sure you could test the finished compost for GMO.
This what is so scary about the GMO, we are not sure where it is , how to test for it or how to destroy it.
I would agree with gardengal48, Hotter the compost, the purer the finish compost.

Technically, since we don't live in a vacuum it would be near impossible to create 100 percent pure organic compost,
although by spending enough we could set up a sterile environment under lab conditions to do so.

my advice try your best and let compost happen

"Hotter the compost, the purer the finish compost"

This is misleading.

The ideal composting temperature is about 130F. It can get up to 140F but after that ALL the organisms are being destroyed, including the ones that are doing the composting. So turn the pile to redistribute the material and to drop the temperature. It's important to have a composting thermometer and to use it.

"Hotter the compost, the purer the finish compost."

I really like the idea that hot composting is needed to somehow purify GMOs. Since you guys are making this stuff up as you go, how about a definition of "pure". That should be interesting.

Even the organizations that set standards for Organic farms don't insist that compost inputs all have to be Organic. [handy tip: you can distinguish organic (as in, organic matter, organic compost) from Organic (grown without chemical inputs) by capitalizing or not.]

A few other thoughts from an environmental chemist:

1) GMOs have slightly different DNA and differences in various proteins, etc. as a result of the modifications. These essentially break down into their component parts in the compost. If you are concerned about seeds, just pull up any volunteers. But there is really nothing else here to contaminate the garden.

2) As far as chemical contaminants, the dose makes the poison. Actually composting methods are used to biodegrade contaminants like gasoline. But even if there are contaminants present in your compost inputs - traces of pesticides on food scraps for example - keep in mind that they do biodgrade at least somewhat in the compost; and you're not eating the compost anyway; AND it is very unlikely that garden plants could even find, much less take up, any residues at levels that would be significant for human health. If you're eating Organic produce, there aren't any going into your pile; and if you're not, you're getting a far larger dose from the part you ate than from plants grown in soil amended with compost made with the scraps.