I don't know about geometric measure theory in particular, and I'm not sure if anyone on this site does. But I can offer one answer to the more general question "Do math departments still hire people working in Specialty X"? In particular, here's one source of information that might help you answer your question:
Identify the names of the leading geometric measure theorists in the field, and/or the particular researchers you might be interested in working under.
Look them up on the Mathematics Genealogy Project, and find out the names of students they have graduated in the past 5-10 years.
For each student, type in "[Name of Student] Math" into Google; typically, if they are employed in some math department somewhere, either their website or their department's website will be the first hit.
If you know people in the field, you might also ask them directly for their impression of the job market, especially if they or their students were on the job market recently.