There is certainly nothing wrong with saying, “I am a sinner saved by grace.” The people who object to that term want to stress that we are now saints with a new position by virtue of God’s grace at work in us. That is certainly true. We don’t really have to make a choice. Both sides of this are true:

We are sinners saved by grace.
We are saints who sometimes sin.

One statement emphasizes the continuing reality of sin within the life of a believer. The other emphasizes God’s gift of a new life, a new creation, and a new position. Martin Luther was fond of the Latin phrase, “Simul Justus et Peccator,” which means “At the same time righteous and sinners.” That seems like the right balance to me.

We are truly justified by God’s grace.
We are truly sinners as long as we live.

We don’t have to choose between these two truths because they are true of all believers everywhere all the time. R. C. Sproul summarizes it the way:

“In and of ourselves, under the analysis of God’s scrutiny, we still have sin; we’re still sinners. But, by imputation and by faith in Jesus Christ, whose righteousness is now transferred to our account, then we are considered just or righteous. This is the very heart of the gospel.”

You are a sinner saved by grace and a saint who sometimes sins. As long as you hold to both sides of this great truth, you will be on solid ground.