Wouldn’t any true believer think that he was a member of the Church created by Our Savior? That to the extent others disagreed on basic doctrine they were in error?
That's just it, though. Doctrine isn't just something we come up with off the cuff. Doctrine has a source - the Word of God. Rome claims that its traditions are on par with Scripture, but (amusingly) does so on the basis that Scripture says so in II Thessalonians 2:15 (which it doesn't of course, the "traditions" Paul mentions were orally preached analogs to the written truths appearing in his epistles). However, no professing church has any authority apart from the Word of God - The Bible defines what "the church" even is. The Word of God is what gives churches their authority to teach and preach and conduct matters internally within their own membership - not "tradition" (which can mean anything, and HAS meant just about anything over the past 1600 years of Catholicism). The measure of whether a professing Christian is doctrinally correct or not correct has nothing to do with whether they agree or disagree with some denomination or group. It is measured by how their theology stacks up against the Bible as it is systematically exegeted.
Any true believer in Jesus is a member of the Church. That's by definition.
This is a basic point of confusion between Catholics and many other Christians. When I say that the RCC isn't the Church, that does not mean that I am trying to take the claim of Church for myself or my synod.
The "Church" is not an earthly institution, but the entire community of believers in Jesus. The Nicene Creed is a good example of that statement of faith.
That to the extent others disagreed on basic doctrine they were in error?
Errors will be burned away at the time of judgment. Errors do not kick you out of the Church.
Simple set theory can help here. Not everyone in the Roman Catholic Church is a true believer. This is true for all churches. Membership in a "church" does not qualify someone for membership in the "Church".
Similarly, there are true believers who are not part of the Roman Catholic Church.
How can the RCC be the Church, when parts of the RCC are not part of the Church and when parts of the Church are not part of the RCC?