No popup notifications from NetCommunity email services when using Gmail on iOS

I can't seem to find anyone else with this issue so I'm posting to the community form here: I do not get email popup notifications on my iPhone when using the Gmail app. This only happens when I receive emails from myschoolemails.com or myschoolapp.com, both of which show mailed-by: blackbaudemail.netcommunity1.com in the header. I do not have this issue with any other platform (Android or desktop browsers), and not with any other email senders, and I can replicate this issue with brand new iOS accounts, new Gmail accounts, and fresh installs of iOS on iOS devices. The emails are received, as the Unread badge icon (in the red circle) increments by one when the email comes in, but no popup notification appears. This is especially an issue because sometimes this is used to send important information (e.g. school closings), but when the popups do not appear they are delivered silently.

I suspect it's an issue between Blackbaud and Apple Push Notification Service. I even get popups when I get a support email from blackbaud.com, so it's not a Blackbaud-wide issue. This only happens when emails are mailed from netcommunity1.com. I suspect this could be an issue with Blackbaud's use of an HTTP header, RPCampaign, that not confirm to any RFC standard (it should be X-RPCampaign) but I can't test this on my end.

Can someone confirm that they receive popup notifications in Gmail on iOS devices from these web servers?