The grammar in the Greek sentence suggests the Early Christians gave themselves primarily to two things: teaching and fellowship. The two must happen simultaneously in the church. Think about it this way: teaching without fellowship is a dry, academic exercise; but fellowship without teaching is merely a social club.
The Early Church was first a learning church. It was certainly more than that but not less than that. What they believed and taught about Jesus defined the rich sense of community they enjoyed. And yes, doctrine and theology mattered to them. In fact, the apostle Paul often warned about false teachers creeping into the church and leading people astray. For example, as Timothy was getting ready to assume the role of senior pastor in Ephesus, Paul writes these words to him,
As I urged you when I went into Macedonia, stay there in Ephesus so that you may command certain men not to teach false doctrine any longer nor to devote themselves to myths and endless genealogies. These promote controversies rather than God's work―which is by faith. The goal of our instruction is love, which comes from a pure heart and a good conscience and a sincere faith. 1 Timothy 1:3-6
Paul also told Timothy to "preach the Word" (2 Tim. 4:2). A church that drifts away from the centrality of Scripture is destined for shipwreck. I've seen too many of my colleagues abandon the teaching of Scripture for the sake of relevance, replacing the meaty exposition of God's Word for milky substitutes that barely nourish the soul.
I've also seen churches walk away from a view of Scripture that affirms its Divine authorship.
For the record, I believe in the infallibility of Holy Scripture, that it is totally inspired by the Holy Spirit from Genesis to Revelation. And because "all Scripture is God-breathed" (2 Tim. 3:16), it is also authoritative. It tells us who we are as a church, why we exist, where we are going, and yes, how we are to live. The origin of Scripture is not in man, but "men spoke from God as they were carried along by the Holy Spirit" (2 Pet. 1:21).
The church I've always wanted is at least devoted to the teaching of God's Word. What about you?