I'm an activist for software freedom and I refuse to use non-free software in my life, as a matter of principle. When I'm forced to do so it's certainly very humiliating for me.
Besides, I don't work for a company, but in the public sector (which by the way I think it should not impose non-free software nor secret protocols into the citizens).
It can be, yes. For someone who is a strong believer in and advocate of FOSS, who makes her/his livelihood developing FOSS for a FOSS software company, to be forced to use proprietary solutions where there are reasonable FOSS alternatives can be very disheartening, demoralizing, and even humiliating.
I am not sure still why it is humiliating specifically - disheartening sure, demoralizing makes sense. But why would it be humiliating if you are not the person pushing that the paid / non FLOSS app be used in the first place?
Isn't this also a good chance to evangelize an alternative to whomever you are speaking with?