Clients first.
I do support, 24/7, I get s..t from anything, including WhatsApp. After that I have the chance of reorganize the requests into my favorite task manager.
Customers just want to know you are there...
Clients first, and always replay via email. Be consistent in accept from any channel, replay, report, notify via email.
This also applies to colleges as well as clients.
If "meetings" implies "work" (which it _strongly_ does to me), then you use whatever the meeting requires.
Your job is to do the work. Not to dictate and ensure FOSS purity amongst co workers and clients.
On your _own_ hardware and for your personal comms, sure - knock yourself out. I have a similar refusal to use Facebook/Twitter for social/personal stuff. It means I get "left out" of some things where no-one remembers to mention to me an event organised exclusively thru FB, and I'm OK with that. Your boss should not be OK with you missing meetings or pissing off clients because you refuse to use Skype. Deal with it, perhaps while encouraging change from the inside without making annoying demands on everybody else - or quit. (Or be a jerk and wait until you get fired for it...)