Folks at Harvard support labor unions… everywhere except at Harvard
blogs.harvard.edu
blogs.harvard.edu
The only exception that these folks allow is that workers (other than themselves; the AAUP functions as a union to some extent) should not be unionized at their own university and/or that the university should not have to pay what already-unionized workers are demanding.
It'd be pretty inauthentic if people who support the existence of labor unions believe their workers or community members shouldn't unionize.
On the other hand, nobody is under obligation to automatically pay whatever unionized workers are demanding. That wouldn't even be a negotiation, and negotiation is what unions are for. That some strikes are overreach and won't receive universal support isn't some kind of argument against the existence of labor unions. The reality tends to be a lot more subtle.
Look at articles in the student newspaper:
"More than 100 Harvard Faculty Signed Petition to Support Strike" http://www.thecrimson.com/article/2016/10/25/faculty-letter-...
"Hundreds of Students Leave Class to Support HUDS Strike" http://www.thecrimson.com/article/2016/10/18/huds-supporters...
Greenspun's rhetoric is an embarrassment.