That's only half the objection. I gave a expansive response in my post to you #209. I recall no engagement by you with that post at all.
For sure, the multiplicity of interpretations advanced by the SS adherents is to us very clear proof that Scripture is NOT 'self-interpreting.' But even more, as I noted (209), with the advent of the Protestant idea of SS, for the first time Scripture was divorced from the notion of an accompanying authoritative (human) teacher. And for the first time there was abandonment of the sense that visible division in the Church is something Scripture condemns.
Scripture gives an illustration of a division in views in Acts 15. Some thought that Gentiles needed to be circumcised (and when your Scriptures are the OT, they had much to search for in support). Others thought that was not necessary. Rather "letting Scripture interpret itself" they met and made a decision binding on the entire church. This model was followed for the next 1500 years. Granted, there were some who splintered off (e.g,, Nestorians, the Monophysite churches in the 5th century), but in the main considerable unity was preserved until the 11th century.
With the advent of SS, even within Luther's time he observed the rapid increase of conflicting beliefs and practices ("as many sects as heads" was his wording" at one point). And when different groups separated into rival theological camps (Luther v. Calvin. v. Zwingli, on onward) there was no mechanism left by which to resolve the conflicts. Protestants claim to exalt Scripture above all else, but then at the same time tossed out the very model Scripture gives us for resolving disputes and avoiding division.
Both of Luther's innovations were premised on things not directly founded in Scripture. SS was really the only position left after Luther rejected Church authority; and once Apostolic Succession was tossed out as the Scriptural and historic benchmark of authority, conciliarism was made impossible. Paul admonished those in Corinth for dividing into camps according to which person had baptized them. 15 centuries later "I belong to Luther," "I belong to Calvin" and "I belong to Zwingli" (who each espoused differing views on baptism) parallels the very denominationalism Paul was urging be avoided.
And this from those who are supposedly following Scripture. And the response about some unified "invisible church" is just more invention; such a notion is completely absent in history.
That's the problem.
and yet when it comes to their own magisterium, they are willing to allow for non unanimity.
On matters of faith and morals which have been defined, no, there is no room to say "on this point, the truth is ___" and say so contrary to Church Teaching. And while there may be differences of view over some matters not yet formally defined, the point is such are rarely cause for visible separation! I can't say the same for the SS crowd.
IOW, it doesn't HAVE to be unanimous.
If division were avoided, I'd take less issue.
Then rightly DIVIDE the Word of Truth!
Matthew 4:18 Douay-Rheims 1899 American Edition (DRA)
And Jesus walking by the sea of Galilee, saw two brethren, Simon who is called Peter, and Andrew his brother, casting a net into the sea (for they were fishers).
Note it's the Catholic version!