Ummm… Boy… Deep breath

Zero GMO genes commercially available cause infertility. The only infertility GMO gene was developed by the USDA-ARS as a way to prevent the spread of GMO genes into the environment. Public outcry shot that one down, so now we have widespread GMO contamination in some species…

Some species hybrid production utilizes male sterility. For example hybrid onions utilized cytoplasmic male sterility. This is a naturally derived mutation that is passed on in the cytoplasm (mitochondria and chloroplasts). This DNA only comes from one parent an is an exact copy (put your punnet square away).

A different example of “sterile” hybrid is gynecious cucumbers. Cucumbers can be all female (gynecious) or monoecious (male and female flowers on same plant) . These are hybrids that are produced by by crossing two gynecious lines using silver thiosulfate to convert one parent to male bloom.

Both of these types will produce seed if crossed with fertile pollen from another plant.

Most hybrids can have seen saved from them except for triploids. Triploids like seedless watermelons are sterile because they can’t form gametes correctly. Diploid lines are crossed by tetraploid lines to created triploids. Triploids in nature is usually sterile (with exceptions of course like the the Amazon molly cause life finds a way).

An OP variety is a partially inbred population. In tomatoes for example. You can easily make these from a hybrid by saving seed for a few generations. The level of heterozygosity decreases by 50% every generation. So a F1 hybrid is 50%, F2 is 75% uniform, F3 is 87.5% uniform, F4 is 93.75%. This is where most OP varieties are. As tomatoes are mostly cleistogamous, no extra effort to exclude pollinators is needed