One of the odder notions in D&D was that all intelligent creatures of a given alignment shared a secret language of passwords and gestures. There didn’t seem to be anything too secret about this, since there were only three alignments in BECMI. If implemented, it would circumvent most of the language differences in the fantasy world, and Chaotic characters could talk to practically any monster. It was also strange that a character who changes alignment immediately forgets the old language and learns the new one. Unsurprisingly, many gaming groups simply ignored alignment languages, not knowing what to do with them.
Fortunately, Gary Gygax clarified his intention for this mechanic in a posting on Dragonsfoot in February 2007. Alignment languages were supposed to be akin to Hebrew for Jews or Latin for Catholics, a ritual language known only to those initiated in a belief system. Only clerics would be fluent in such a language, while non-clerics would have “only a limited vocabulary,” and not be able to convey or understand much.
With this understanding, we might propose a more workable usage of alignment languages. Non-clerical members of an alignment may each recognize a few phrases or signs of the alignment language (not necessarily the same ones!), so they may sometimes signal to other creatures what their alignment is, but nothing more.
Clerics (and perhaps a few well-educated laymen) are formally trained in their alignment language, perhaps becoming fluent at Level 3. They may converse secretly with other clerics of the same alignment.
This leaves the problem of alignment change. The business of immediately forgetting and learning alignment languages may be understood to apply only to magical changes of alignment, such as donning a Helm of Alignment Change. Natural changes of alignment, if allowed by the DM, need to be handled more cautiously.
Realistically, we should not expect a character to instantly forget his old alignment language, but perhaps it will become distasteful for him to use, as a reminder of his old beliefs. Non-clerics should be able to recognize the old alignment language, and clerics should be able to understand it, albeit less fluently over time. Clerics will absolutely refuse to speak in their previous alignment language, for fear of divine wrath or betrayal of principle. Non-clerics might dare to use a few signs of the old language in mockery, but will not otherwise communicate in it.
Clerics may become proficient in their new alignment language after they progress to their next level, but they never gain the fluency they had in their old language (unless they change alignment before reaching Level 3). Non-clerics never learn more than a couple words or gestures of their new alignment language. This diminished ability in the new language compensates for their residual knowledge of the old, so there is no substantial benefit to changing alignment.
It is important to establish that alignment changes are rare, so an NPC or monster who understands an alignment language is almost certain to be of that alignment. Clerics who speak an alignment language and non-clerics who use it respectfully are definitely of that alignment.