This is a very wet gingerbread batter.
Should I substitute the applesauce for (some portion of) the eggs, butter, molasses, or beer? Does it matter?
Are you channeling your best self with this comment? (If you're not sure, check out our Code of Conduct.)
Applesauce can be substituted for OIL in a recipe, not for eggs, molasses, buter, or beer
hardlikearmour is a trusted home cook.
I'd probably start by replacing the beer with applesauce -- depending on how wet the batter is it could work as a 1:1 replacement, but you may need to add extra liquid if it's too dry. You can replace melted butter with applesauce as well, but I think you'll have less textural change by replacing the beer. If you go with the fat replacement, start by only substituting half (or less) with the applesauce.