I have an email forwarder on my personal domain that forwards to my gmail address, and gmail lets me send email as if it were coming from that address. Seems like it's the same result, and they're not blocking that.
Just counter this with a little more anecdata, I'm a regular GP visitor in Australia and have found them to be great. The only antibiotics I've been prescribed in the past decade were for a particularly persistent parasite infection.
I've read a few older books with my kids that contained mildly questionable things, like a boy saying that girls can't do certain things, but I much prefer having that awkward conversation about how things used to be, over tossing it all out and pretending things were never any different.