For me, the book of Acts is key to this question.
Acts 2 tells us the Lord added to the church daily those who were being save.
The church isn't a building, but a body of believers. However, most churches meet in a building.
In Acts 2v47 it says they were praising God.
If we then change the service, that was meant to be used for praising God into evangelism, it is not God centred, but now man centred.
Let's look at false religions.
When they meet together, is it for outsiders or for those involved in their own beliefs? Do they change their meetings for outsiders, or is it still as it always is?
So, should Christians change their worship of God to accomodate unbelievers? No.
Acts 4 the apostles preached Jesus in the temple.
I would assume those in the temple had some godly conviction, or they would not have been there.
Acts 8 Philip went to Samaria and preached Christ to them. It doesn't say he went into a building, but to the city.
No doubt others will point out other scriptures such as 1 Cor14, James 2 etc.
For now I've said enough. Don't want to be too long. God bless.