When we affirm in the creed a “holy catholic church” we are not saying that every church, or especially our church, is secretly part of the Roman Catholic denomination or that we are in submission to the Pope in Rome. What the word means is “universal.” The early Chruch Bishop Ignatius of Antioch used the word this way, somewhere around AD110, “Where Jesus Christ is, there is the catholic church.” In this sense we mean that the Holy Spirit is at work in God’s church, revealing and glorifying Christ. We claim a fundamental connection between all churches where that happens. This idea unites all true believers into one faith. In this sense, yes, we are “secretly” (as in mystically and spiritually) united with Christians in many different denominations, including many within the Roman church along with Lutherans, Anglicans, Baptists, Mennonites and so on. We are united because, by faith, we have received the Holy Spirit and He is one. There is no Lutheran Holy Spirit distinct from an EC Holy Spirit. He is one and we confess that He works in and through the churches making us one and linking all true saints together, hence: “the communion of saints.”
We talk about baptism in this context, as well, because baptism is the initiation rite into the universal church. Much like a wedding starts a new family, baptism is when you join up. God is at work in both ceremonies and going on from them, we expect the Holy Spirit to convict, encourage and guide us towards a faithful application of what those ceremonies signify. At baptism we invite the Holy Spirit to do what this part of the creed affirms in us: to make and remake our identity in union with God’s people across all time.
To sum, this part of the Creed is about the Holy Spirit giving us corporate and personal identity. So, in professing our belief in the Holy Spirit’s work making “one holy catholic church” we profess our membership in the universal (“catholic”) church as defined by the sanctifying (“holy) work of God’s Spirit in our midst. Second, we profess a common personal identity shared with all believers (“the communion of saints”) and found not in ourselves but through our adoption by the Holy Spirit, wherein we cry, “Abba, Father!” to God as Paul attests to the Spirit doing in Romans 8.
Passages: Mt. 7:15-20, 12:22-37, 1 Cor. 12:3, Mk. 9:38-41, Acts 10:34-11:18, 19:1-7, Rom. 8:12-17, Eph. 2:11-22