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Yes, gmail is like that. I recommend against anyone using it if they really want to receive mail from anyone other than those using gmail. It's a very common problem, and not much that you can do about it either - google around and you'll see nightmares about it.
I've setup a SPF, DKIM and DMARC record for my mail. I ensured it looks pretty good with a mail tester (mail-tester.com if you're interested). The thing looked really good.
At the time of writing this small email, I haven't had any problem with Gmail rejecting my emails for any obscure reasons or any mail providers thanks to my ISP relaying my emails :p
- -- Mathias B. GPG: B662 E39E 8971 8E6B 8960 893C 4577 D41D 2F68 4552 (Public key: http://l4p1n.ch/info/pk)