If the drum manufacturer used BPA as a stabilizer there may be a concern. BPA is known to leach out of the plastics that contain it and is known as a health concern for humans and currently the amount that humans should consume is zero.
What is unknown is the dose humans might tolerate, whether BPA in the soil is taken up by plants, or any other useful information about it.

If you are looking for a definitive study on the question then I seriously doubt you will find one. Even the BPA issue has mixed results and many unsubstantiated claims.

But lots of folks garden in plastic barrels and have for decades with no notable concerns. They are constructed of what are called hard plastics rather than the soft degrading plastic so have different components.

Further the "leaching into the soil" Issue has been studied with other, much softer, materials and found to be relatively minimal. Actual absorption by the growing foods is even less - if any.

Personally, just as with all the other plastic gardening containers available, I am quite comfortable using them and have for years. But you have to deal with your own comfort level so why not research what synthetic chemicals may be used in the construction of hard plastics - lots of online info available - and then decide if you can be comfortable using them.

Dave