Are organic vegetables GMO free ?

yes. see http://cli.gs/rEXdWW

You have no idea how much I wish the answer is different, but. . . no, "organic" soy products are not all made without GMO products.  The problem is that there are very few companies who are growing truly organic soy -- and certainly not enough of them to supply the need and demand.

The problem is exacerbated by the fact that GMO crops cross pollinate; we see it with corn, wheat, and soy.  There is currently no way to prevent GMO crops from infiltrating non-GMO fields and polluting them with their DNA.  This is a very sad situation, and one with all the organic farmers warned would be a hazard.  Unfortunately, greed won out -- and today there are no reliable sources of truly GMO-free soy.  The ones that still exist are imperiled by the intrusion of nearby GMO crops. 

Now, in fairness, the GMO crops CAN be raised organically (that is, without pesticides or organophosphates applied to them) and still meet the standards for organically grown crops.  But they are still GMO soy beans, even if they are from the time of planting to plate handled according to current organic standards.

Perhaps one day we may find a way to turn the situation around, but until then, the answer to your question is, sadly, NO.

Brightwings makes a worthy attempt to respond to the complexities, but sadly is misinformed.

My simple answer "yes" refers to the basic question, are GMOs excluded from organic production? Under federal rules, any product labeled organic cannot muct exclude the use of GMOs-despite Brightwings statement, organic crops cannot be grown from GMO seed (even if the farm's practices are organic). 

It is true that GMO contamination is widespread and inevitable, so if purity is the issue, "GMO-free" may be difficult to attain or verify (asking organic producers to verify this would mean huge seperation and testing costs, which should be borne by the biotech industry-after all, it's their crops that are polluting natural food). But this does not mean that organic crops are made from GMOs - quite the contrary - any organic soy is, by law, made without GMOs (I also know of no major supply issues, many companies sell many organic and/or non-GMO soy products, and the cost of these products has not dramatically increased since the advent of GMOs, suggesting that supply is not a major problem).