The short answer to your question is probably "yes", with some caveats.  There is a lot more information on vegetable gardening in galvanized tubs from people wanting to sell them to you than there is evidence-based research on the subject.

Galvanized metal has a zinc coating with a small amount of aluminum and cadmium.  Zinc can be toxic in large quantities, although is it a necessary micronutrient. Apparently it may tend to leach out of the metal and into the soil if the pH is less than 5.
This means that knowing the pH of your soil is important, and I wouldn't plan on safely growing acid-loving plants like blueberries or maybe even potatoes (although 5 is a bit low for potatoes). 

Cadmium and aluminum are also potentially toxic but less soluble than zinc.  One of the sources I checked made the excellent point that a new trough is less likely to leach elements than an old rusty one.

From Oregon.gov "Food Safety Rules"

"4-101.15 Galvanized Metal, Use Limitation.
Galvanized metal may not be used for utensils or food-contact surfaces of equipment that are used in contact with acidic
food."

An answer to the same question in 2014 from another Extension volunteer:
Galvanized Container Gardening - Ask Extension

In the "better safe than sorry" category, an University affiliated author recommends NOT growing vegetables in galvanized containers (below).
Growing edible plants in galvanized containers | Elisabeth C. Miller Library (washington.edu)

For practical purposes, I think using new (not rusty) troughs for growing vegetables with neutral or slightly acidic (6.5-7.0) soil is likely fine.  For extra caution, using a plastic liner or a rubber trough might be safest.  Don't forget to provide for drainage. If there is a question about the pH of your water, take that into consideration.

Thank you for asking Extension about growing vegetables!  More people should do it, in my opinion.