Sorry for the delayed response. We don't have any known issues with Cloudflare. Many of our user use it, as do we.
I just went to your site.. *beautiful site* by the way.. I really like the layout and design. I found the Invite at the bottom and sent myself an invitation. Below is the image from my 'receiving' account, which is exactly as I'd expect:
That's the normal behavior and it seems to be working as expected there.
Can you please make sure when you send the invites that:
a) You click the "invite" button to the right of each user and
b) Hit the blue "Done" button after you've selected the recipients
I hope that helps, but if you still have issues, just let me know.
Thanks,
Alex