Thanks for your answer, but the “Church” is not based on people referring to its members as Christians.
What is your assessment of the beginning of the "church"...if that isn't too much of a derail?
Secondly, there is no such thing as the “Jewish Church”.
In a sense, I agree...though those who are Jewish, nationally, could be referred to as a Jewish church. Though now I think of the church as those "in Christ" without regard to nationality.
Thirdly, the Spirit baptizes us into Christ.
I guess you are referring to 1 Cor 12:13..."For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit."
But that verse needs to be liked with 1 Cor 6:11..."And such were some of you: but ye are washed, but ye are sanctified, but ye are justified in the name of the Lord Jesus, and by the Spirit of our God."
There is a "wash" involved with the "and the Spirit of God".
The baptism is in water and the gift of the Holy Ghost, also called the baptism of the Spirit, comes later. Just as Peter laid it out in Acts 2:38.
The Apostles of Jesus Christ baptized people in water, while He was living.
And continued to do so after His death and resurrection, as Jesus did command it in Matt 28:19.
And if he refuses to hear them, tell it to the church. But if he refuses even to hear the church, let him be to you like a heathen and a tax collector. Matthew 18:17
Good use of the term "church".
I'm surprised Jesus didn't say "synagogue".
Perhaps prophetically looking ahead?
As Jesus' disciples weren't meeting in their own building as a congregation, the term "church" just implies adherents to a certain set of doctrines when used from Jesus' times.
Now we say "Christian church" to differentiate it from other doctrines.
But in Jesus' times there was no other doctrines besides Judaism for the children of God.
It would be sad indeed to think that no one was saved through the ministry of Christ preaching the Gospel.
Indeed, it would be sad.
But the Israelites had the Law of Moses for their salvation in the times before Christ's resurrection.
As they were still walking in the flesh instead of the Spirit, until they could kill and bury their old selves at their water baptism into Christ and into His death and resurrection, it wouldn't be till after Jesus was killed, buried, and resurrected that they, we, could walk in the Spirit...and be a "church" of our own.
The important thing is that you are part of the Church now, by believing and obeying the Lord Jesus Christ.
Amen to that, to the glory of God and to the name of Jesus Christ.