The hormone issue was set to rest a long time ago. The medical journal that published the study retracted it (with apologies) when the results could not be replicated, and multiple other studies have shown that soy is beneficial. In particular, the lunasin peptide is highly beneficial in reducing inflammation and repairing damage to the epigenome which controls cell function. There are still people quoting the "bad soy" idea but there are no scientists of any high repute who are even debating it at all. Go to pubmed.gov, for example, and search under lunasin/cancer and see how many studies there are since 1998. And that doesn't even cover the cholesterol-reducing effects.
Soy has been nature's protein for 5000 years, and countries with high soy diets have lower rates of breast cancer and lower rates of recurrence in those patients who do get it. (Major studies were done to this effect about 8 years ago or so.) Only when these countries start processing the soy the way we do in the US, including a reduction of lunasin or poor techniques to extract it, do their cancer rates start to increase.
There are few doctors who aren't up on this, and may still say "stay away from it" and there are average citizens who cling to the notion that it's bad for you, just as we cling to the idea of "8 glasses of water a day" even though that was never, ever proven and is just a made up number that's been repeated so often, people think it's true. Same for the idea that it gives men enlarged breasts. No it doesn't. Put it in the urban legend category.
The issue with soy milk is not whether it's organic - it might be grown organically, but you don't know if it's from genetically modified seeds which can reduce the amount of lunasin in it. (And there are terrible sources of poor quality lunasin, just as there are poor sources of every other vegetable, fruit or other food product.) You also don't know how it was processed - and that's the killer with soy. Alcohol, hexane, etc. - no matter that it was grown organically, the processing is not well regulated.
I eat plenty of soy from a non-GMO source and with a very high lunasin content, and I've been in many training sessions with the epigeneticist who discovered it, as well as other scientists. My breast health has improved (says my doctor, who is very happy after all my abnormal mammograms in the past) and my overall immune system is strengthened. Same for tens of thousands of other people.
The only other question about soy milk is how much soy is in there - how many grams? And is it in an absorbable form which allows the various nutrients to survive digestion - that's a big one.
So it's not going to have anything bad in it from a hormonal standpoint. Whether it meets your nutritional needs is something else again. But I don't see any reason to avoid it if you can verify the source of the soy and the processing involved.