We have a hypersensitive smoke alarm in our house. It goes off all the time. But I think it is better to have a smoke alarm that is too sensitive than to have one that isn't sensitive enough.
As believers, we want to have a working conscience. The apostle Paul warned, "Now the Spirit expressly says that in latter times some will depart from the faith, giving heed to deceiving spirits and doctrines of demons, speaking lies in hypocrisy, having their own conscience seared with a hot iron" (1 Timothy 4:1–2).
If your conscience is sensitive, that is good. You don't want it seared as though a hot iron had been applied to it.
I heard a story about a man who went to see the doctor with two severely burned ears. The doctor said, "You have to tell me—how did this happen?"
The man said, "Let me explain. I was ironing a shirt when someone called me on the phone, and I answered the iron instead of the phone."
"That is horrible!" the doctor said. "That explains one of your ears being burned. How did you burn the other?"
"They called back."
We don't want our consciences to be seared. We want them to be sensitive and open to the work of the Holy Spirit.
We have this promise in 1 John 1: "But if we walk in the light as He is in the light, we have fellowship with one another, and the blood of Jesus Christ His Son cleanses us from all sin" (verse 7).
Because Jesus died on the cross and met the righteous demands of God, you can approach the Lord at any time, no matter what you have done, if you will confess your sin and ask for His forgiveness.