One of the primary ways the church has understood this over the years is the presence of the Holy Spirit in believers. That’s a good way of thinking. When we add the instructions, we may begin to see a problem. Based upon the words of Jesus, we could simplify the instructions (which makes sense in light of the New Covenant) to love God and love others.
It is, however, this combination that can cause a person (especially a non-believer) to wonder if the New Covenant has actually come. Depending on your circles (whether of happenstance or decision), we have seen our brothers and sisters behaving in ways that do not seem to be motivated by the love of God or others.
As we say we are Bible-believing people, the Bible is going to be one of the first places that non-believers (in particular, those who seek to not believe) go to check what Christians are supposed to be. This is what we should be thinking about as we read the Scriptures.