And why won't two Baptist touch your beer?
The implication is that neither baptist will drink in front of the other. There is another old joke about various doctrines that different denominations don't recognize, with the punchline being that Baptists don't recognize each other at the liquor store.
Because Baptists, as a denomination, are very very opposed to drinking. When they are together, they are a lot more firm on that rule of thumb.
The scriptural reason is that many Baptists (and other fundamentalists) have focused hard on the biblical admonition in Romans 14:11-21 to avoid doing anything that would make your brother stumble. The idea is that Christianity frees the saved from the Mosaic law (i.e., don't eat pork, etc.). But some in the early church (and it continues today with drinking) believed that God's will was that we shouldn't eat or drink certain things. In Romans 14, Paul notes that for those who have accepted Christ, there is nothing unclean to eat although some may continue to believe that eating or drinking some things is contrary to God's will.
Paul resolves this dispute by noting that there's way more important things - the core doctrine of the Gospel that Jesus was the Son of God, that he came to earth in human form, that he lived a sinless life, that he died on the cross and thus offered his perfect life for our sins, and that he was resurrected after three days - than what you eat and drink.
Nonetheless, if a Christian believes that certain food or drink is unclean or sinful and partakes anyway, Romans notes that that is the same as willful disobedience to God, which is sin. So it's not the actual works or acts that are important, but rather whether the Christian is conforming him or herself to God's will. Doing something that you think is sinful is sin, even though the specific act is not in itself sinful.
Consequently, Paul admonishes Christians not to tempt their brothers & sisters in Christ by eating or drinking something that other Christians consider sinful. In other words, avoid drinking in front of someone who could be tempted or led astray by your alcohol consumption. Place their needs ahead of your own. At the obvious level, don't take your recovering alcoholic buddy to a bar and grill for dinner. At the more subtle level, the person you're drinking in front of might be a closet drinker or otherwise on the edge.
With all that background, if you eat or drink something in light of repeated statements in the NT that there are no unclean foods for Christians, don't do it in front of other Christians (particularly baptists) who might consider it sinful.
Same as how do you keep a Mormon from drinking your beer when you take him fishing? Take another Mormon along.