I am of the opinion that it probably doesn't help in most circumstances, and that most people will understand if you politely and non-judgmentally decline to drink (there are a hundred ways to do that without being offensive or snobbish). Sometimes, though, I do think that it might hinder your witness not to drink. Case in point: in Albania, where I have been on mission trips three times and have stayed with local families every time, there is a traditional drink of hospitality in the villages called raki. Raki is basically moonshine, and although I'm not sure what proof it is, it's probably triple digits. It's disgusting, potent, and a gesture of hospitality and good health to guests. So if you refuse it, it's insulting to your guest and will hinder their receptivity to anything else you'd say, no matter how loving. So I drank it, at least a little bit, even in the morning when it was served with my breakfast and Turkish coffee! When the host would go to another room, I'd pout it out a window or something, but I always tried it. But does this happen in the same way among Americans? Probably not: people understand when you say, "No, thank you, I don't drink."
The argument from those who insist on their right to drink is that it breaks down social barriers with friends and acquaintances with whom you are developing a friendship, and it leads to a shared experience in which more openness and honesty is likely. The argument from those who insist on not drinking is that drinking, even lightly, harms the consciences of those for whom drinking is unconscionable, i.e., it causes them to stumble in their faith. Further, they argue that drinking blurs the line between being in the world but not of the world.
Jesus, as he often does, blurs modern distinctions. He turned water into wine for a friend's wedding feast. He was accused of being a drunkard (probably an accusation you can't earn without ever taking a drink), and he hung out with drunkards and other "sinners." Most Christians know that what the New Testament condemns is drunkenness, not drinking. In fact, in one place, the apostle Paul urges his disciple Timothy to drink a little wine for his stomach (1 Tim. 5:23). I believe the best place for us to turn is Romans 14 and 1 Cor.8. Interestingly, the discussion at the time wasn't alcohol, but meat sacrificed to idols.
Romans 14:1-3, 15-23 Accept him whose faith is weak, without passing judgment on disputable matters. 2 One man's faith allows him to eat everything, but another man, whose faith is weak, eats only vegetables. 3 The man who eats everything must not look down on him who does not, and the man who does not eat everything must not condemn the man who does, for God has accepted him. . . . 15 If your brother is distressed because of what you eat, you are no longer acting in love. Do not by your eating destroy your brother for whom Christ died. 16 Do not allow what you consider good to be spoken of as evil. 17 For the kingdom of God is not a matter of eating and drinking, but of righteousness, peace and joy in the Holy Spirit, 18 because anyone who serves Christ in this way is pleasing to God and approved by men. 19 Let us therefore make every effort to do what leads to peace and to mutual edification. 20 Do not destroy the work of God for the sake of food. All food is clean, but it is wrong for a man to eat anything that causes someone else to stumble. 21 It is better not to eat meat or drink wine or to do anything else that will cause your brother to fall. 22 So whatever you believe about these things keep between yourself and God. Blessed is the man who does not condemn himself by what he approves. 23 But the man who has doubts is condemned if he eats, because his eating is not from faith; and everything that does not come from faith is sin.
1 Corinthians 8:8-13 8 But food does not bring us near to God; we are no worse if we do not eat, and no better if we do. 9 Be careful, however, that the exercise of your freedom does not become a stumbling block to the weak. 10 For if anyone with a weak conscience sees you who have this knowledge eating in an idol's temple, won't he be emboldened to eat what has been sacrificed to idols? 11 So this weak brother, for whom Christ died, is destroyed by your knowledge. 12 When you sin against your brothers in this way and wound their weak conscience, you sin against Christ. 13 Therefore, if what I eat causes my brother to fall into sin, I will never eat meat again, so that I will not cause him to fall.But there's also 1 Corinthians 9:19-23:
19 Though I am free and belong to no man, I make myself a slave to everyone, to win as many as possible. 20 To the Jews I became like a Jew, to win the Jews. To those under the law I became like one under the law (though I myself am not under the law), so as to win those under the law. 21 To those not having the law I became like one not having the law (though I am not free from God's law but am under Christ's law), so as to win those not having the law. 22 To the weak I became weak, to win the weak. I have become all things to all men so that by all possible means I might save some. 23 I do all this for the sake of the gospel, that I may share in its blessings.An important question to ask about 1 Cor. 9:19-23 is in what way did Paul become like the ______? In their drinking? The text does not specify. I don't think we can confidently stand on this passage to justify social drinking for the sake of evangelism.
Do I think it's wrong for a Christian to socially (and very moderately) drink? No. Do I drink? Almost never. If some friends invited me to go to the bar with them, and there was no schedule/family time conflict preventing me, I'd probably go and drink Dr. Pepper and enjoy the company of my friends.
But however you feel on this issue, we shouldn't only share the gospel with people when they are comfortable, on their turf, and loosened up by a couple of drinks. Let's share Christ at work, at the gym, with the daycare staff, with the server at the restaurant (extreme politeness and big tips), with the customer service agent, etc. And if you do drink with your non-Christian friends, don't forget to tell them about Jesus.