I think the GNU response is more subtle than "boycott it". In particular, I do not get the impression that GNU opposes someone using software that runs on someone else's server machine
in general. One obvious example would be an HTTP server with PHP scripts, or whatever.
The software running on the remote server could even be proprietary software! For the sake of the person running the server, they should not use proprietary software, but if it is running on their machine and not yours, then it is not your responsibility, and (as I understand the GNU position) not wrong for you to access that software.
Now, if the software is actually a combination of server-side software and client-side software, such as servers that deliver Javascript code to be run locally, then that Javascript software should be Free Software.
But moreover, the GNU concern about running software on remote servers (i.e., "in the cloud"), is not just about the software itself, but about what the server maintainers can and do do with user data. Who owns the data? Can you get a copy of it? Can you get a copy of _all_ of it? How about the implications of the data? For example, you could tell Facebook ten things about yourself, and they could extrapolate a hundred more. Is "your data" the ten things only, and not the additional hundred extrapolations? And, if you ask them to delete "your data", will they? If they do, what exactly do they delete?
So it's really more of a privacy issue, I think, than a pure "free software" issue, but important nevertheless.