I found a way to make it work thanks for this question/answer duo from StackOverflow.
For a vector x for strings formatted "2017-01-01 00:00:00+00:00", do this
using Dates, TimeZones
date_format = DateFormat("y-m-d HH:MM:SSzzzz")
DateTime.(x. date_format)
Not only does this work, it also drops the timezone part, which I intended to do anyway. The original post in the link actually shows a way to split the string before conversion.