In a scientific settings we do sometimes use the prefixes an-, ana-, a- in the meaning of not-containing: anorganisch, anaerob, asozial, anachronistisch,... etc..
This was not the case for substances not containing alcohol. The expression analkoholisch was never used to any significant extent. This makes me believe that proposing this to be an out-dated adjective is plain wrong.
The appropriate German expression for anything not containing alcohol is built using the suffix -frei: alkoholfrei.
Sometimes the adverb antialkoholisch can be seen. This however is a semantically wrong usage of the prefix anti- (agains) probably coming from the noun Antialkoholiker, i.e. a person who refuses to drink alcohol. A beverage can not be this, nor is there any anti-dote to alcohol which would make a prefix anti- valid.