It's your decision - you could say you blocked Gmail. Admittedly, that wouldn't be nice.
Similar to messengers: I am not reachable over WhatsApp, although my family only has that...
I'm not going to shut out my grandparents because they use GMail, and I'm not going to try to convince them to switch off GMail after already being a jerk about not having a Facebook account.
Besides, GMail's limited algorithmic sorting is pretty innocuous; it's Search and Facebook, with their pervasive filter bubbling, that're actually being a problem.
As for messengers... I've never had a problem convincing people to SMS me.
Yeah it's tough. It's the same reason I still use Facebook: Without it, I would be cut off from a large number of family members that only use FB and don't communicate in other means.
That is their choice disrespecting yours one though.
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