Yes, because I believe that I am saved by my works and not God’s grace.

And yes, I would be surprised if Catholic missionaries convert, i.e., they are not easy pickings!
So…you believe you are saved by your works. By saying this, the logical and only conclusion one can reach is that you, apart from God, are solely responsible for your salvation. And, how do you know if you are saved if it is by works? What is the benchmark? How much work? Which works? How can we be “anxious for nothing” if we can not be assured of our salvation?
The love of Christ through faith produces good works…not the other way around. You are confusing Sanctification and Salvation. Salvation is immediate. Sanctification is an ongoing process.
How do you reconcile Ephesians 2:8-9 → 8 For you are saved by grace through faith, and this is not from yourselves; it is God’s gift— 9 not from works, so that no one can boast.
And, The major theme of Paul’s letters is that salvation is a totally free gift – not earned by good works, rituals, or obeying laws. Eternal life is by grace through faith.
In Romans chapters three and four alone, Paul states this principle no fewer than fifteen times. A few examples are:
“Therefore by the deeds of the law there shall no flesh be justified in his sight…” (Rom. 3:19).
“But now the righteousness of God without the law is manifested…” (3:20).
“Being justified freely by his grace…” (3:24).
“…Abraham believed God, and it was counted unto him for righteousness” (4:3).
“But to him that worketh not, but believeth on him that justified the ungodly, his faith is counted for righteousness.” (4:5).
“…God imputeth righteousness without works” (4:6).
Therefore it is of faith that it might be by grace…" (4:16).