What purpose could the prohibition against drunkenness possibly have to a group of people who were unable to get drunk?
If the wine wasn't really wine, then how could they get drunk? Noah certainly got drunk and appears to have passed out from wine. This could be the result of wine fermenting faster in the post-flood environment than it did prior to that. Nonetheless, he certainly became drunk on wine.
Noah began to be a man of the soil, and he planted a vineyard. He
drank of the wine and became drunk and lay uncovered in his tent.
Additionally, there is proverb that prescribes wine and strong drink for those who are in misery. It seems to reach a level of absurity if you think grape juice will help people forget their misery.
Give strong drink to the one who is perishing, and wine to those in
bitter distress; let them drink and forget their poverty and remember
their misery no more.
It seems that "dry" Christians as you call them are fearful that some people among them (in their church or even their children) will become alcoholics if they don't think any alcohol at all is absolutely sinful.
There is also an issue of "the weaker brother". If you're around a group of devout Christians who believe it's wrong to drink alcohol, it would certainly be wrong for you to do so in their midst and be a stumbling block to them.
Finally, there are those whose consciences bother them about things that aren't sin. Eating meat sacrificed to idols was the issue addressed by Paul. People who came out of idolatry had a genuine problem with that. For that reason, Paul was willing to honor them by his own personal choices, lest he make them stumble. Those who have come from backgrounds where alcohol was a vice often have similar reactions against alcohol. For such people, it is best to honor them and not be a stumbling block to them.
We live as free men--free from the law--yet it is wrong to exercise our freedom to the detriment of our brothers and sisters in Christ.