I found this quote of interest, from an introduction to 2 John from a Catholic edition of the Bible, the New American Bible.
For their protection the Presbyter forbids hospitality toward unknown or “progressive” Christians to prevent their infiltration of the community. The Second Letter preserves the Johannine concerns of doctrinal purity and active love in the form of pastoral advice to a threatened community.
They certainly didn’t have us in mind when this was written, but I certainly find it applicable. Shortly, I’ll have a specific situation to speak on.
The translation of verse 9 is suggestive also: “Anyone who is so ‘progressive’ as not to remain in the teaching of the Christ does not have God; whoever remains in the teaching has the Father and the Son.”