Well, there has to be a "by".  Absence of some "by" means Pelagianism.  They must be doing something to actively please God and cooperate with his grace unto salvation.  In other words, a Protestant can attain to salvation by faithfully practicing his Protestantism.  And if that's the case, he has a right to do so.  It's an awful theological mess.

Whether or not strictly infallible, they're clearly binding on Catholics.

How is any Protestant invincibly ignorant of Catholicism?  Have you ever listened to Protestant sermons?  Half their religion is based on trashing catholic doctrine.

Nowadays it seems harder to believe with the internet, but in the past certainly someone could've only heard lies about Catholicism (in, say, Calvin's Geneva) and had no real opportunity to be corrected on said lies.

I mean, most of the serf class never travelled farther than the next village over in their lives. I can't imagine the urban peasantry travelling much farther either unless they worked for traders. If you lived in post-Calvin Geneva there's a good chance the only Catholics you ever met were ones being burned at the stake.

Go beyond that, to 1700s Sweden say. What would some Swedish farmer in Uppland know about Catholicism other than that it was a religion practiced by a bunch of Frenchmen, Italians and Bavarians hundreds or thousands of miles away?

I'm not arguing they were saved, but I don't think they'd have had any chances to learn about Catholicism from Catholics. They'd have to hope for some freak miracle like a missionary sneaking his way through Sweden in disguise, just like how some tribesman would have to hope for the freak miracle of a missionary stumbling upon his tribe in who knows where. So only by God's intervention, but then I suppose all salvation is by divine intervention regardless.