That problem, though mildly annoying to the blog owners affected, has an easy workaround - use a GMail based email address, for comment moderation / notification. That's a quick 15 minute fix.
- Setup a GMail account, if necessary.
- Change the comment moderation / notification email addresses, for the blog(s) affected, to use the GMail email account.
Besides the ease of putting a workaround in place, that problem is not all that severe. The problem with comment moderation / notification email, being filtered, only affects blog owners who moderate before publishing. Owners who moderate after publishing can always use the Blogger dashboard Comments wizard, at their convenience, to moderate.
This week, we realised that the base problem - rejected email because of non GMail based Blogger accounts - may also affect owners of private / team blogs, who have prospective non GMail members. This specific problem probably affects less blogs - but it won't have as easy a workaround.
Owners of private / team blogs, who use non GMail based Blogger accounts, may not find an easy workaround for the problem of Blogger blog membership invitations being rejected by a non GMail email system.
The base problem, as it affects comment moderation / notification, is obvious. The owner of an affected blog will see all comment moderation / notification email, sent to him, rejected by his own non GMail email system. Anybody who owns a blog that's affected will be sending all comment moderation / notification email to the non GMail email system.
The base problem, as it affects private / team blog membership invitations, is more subtle. This problem will affect blogs owned under non GMail based Blogger accounts - and / or when sending invitations to prospective members who use non GMail email systems. Email within Google - Blogger to GMail - should not be subject to the same filtering, since the email will actually originate from a Google server.
With all that, this problem will be more annoying, in that it will involve email rejected by the prospective member email system - not by the blog owner email system. Prospective blog members won't likely be receptive to changing their email addresses, just to receive a membership invitation. Also, the blog owner may not always see the email rejection - and may not know that the invitations are being dropped - and may not be found in the "Bulk" / "Spam" folders.
To avoid this problem, membership invitations, from any affected blogs, will have to have be sent from a GMail based Blogger account. This will require a GMail based Blogger account, added as an additional administrator - and it will involve the known risks of having an extra administrator account. Only administrators can send membership invitations.
This problem will probably have less exposure than the one with comment moderation / notification email - but to the blog owners affected, it will seem more severe. It will actually prevent prospective members, using non GMail based email systems, from joining the blogs affected. And, it will require a blog owner to add a GMail based Blogger account, as a blog member.