How to Engage in Gospel Polemics
Do not dishonour the Gospel of God by harshly condemning others. While Jesus railed against religious hypocrites, he was patient with sinners. And so I think we can categorize two sorts of opponents: those who genuinely disagree with us and those who hypocritically gainsay sound doctrine for greedy gain. I am thinking of the first category here, and 1 Peter provides ample instruction for how we should engage people in this first category.
Give your opponents reasons for your faith with gentleness so that they can only criticize your good behaviour
In 1 Peter, the apostle writes:
but in your hearts honor Christ the Lord as holy, always being prepared to make a defense to anyone who asks you for a reason for the hope that is in you; yet do it with gentleness and respect, having a good conscience, so that, when you are slandered, those who revile your good behavior in Christ may be put to shame. For it is better to suffer for doing good, if that should be God’s will, than for doing evil. (1 Peter 3:15–17).
Peter underscores the need to provide reasons to those who ask and to give those reasons with "gentleness and respect." If this does not happen, then people can slander you in Christ for your bad behaviour which is shameful. It's not a good thing to suffer for doing evil. It's much better to suffer for doing good. So when it comes to defending the Gospel, give your opponents reasons for your faith with gentleness so that they can only criticize your good behaviour.
Argue with ... arguments
Now if you are going to tell someone that they are wrong, you had better have good reasons. Does someone deny the Gospel by their teaching or actions? Then you need to reasonably, gently, and respectfully show why. It's insufficient to say, "You deny the Gospel!" You need to spell out why.
Be gentle by respecting your opponent as a person made in God's image
Gentleness and respect can often look like being slow to speak (don't attack before you know what you are attacking) and being careful with your words (let no unwholesome word come from your mouth but only that is good for edification). Yet we are far too often fast to speak, harsh in our condemnations, and wild with our words. So when we engage people online or on the street, let's remember to reasonably, gently, and respectfully answer those who ask us about the hope within us.