Direct vs Indirect
There is a large amount of disagreement on this question, based on how the wording is interpreted.
For this answer, I'm splitting the arguments into two camps: direct and indirect.
Direct
This argument is that the ring only affects magic that directly targets the wearer. Those siding with the direct argument are the (current) majority, based on a number of replies and upvotes to those replies.
Indirect
This argument is that the ring affects all possible means by which the wearer's alignment could be revealed, even if the magic is only indirectly informing other creatures of the wearer's alignment. There appears to be a minority of such people, but they are firmly disagreeing with the arguments that the ring only affects creatures that directly use magic against the wearer.
Understanding the word "allow"
The disagreement on this question appears to come from different people using different definitions of the word "allow". So, let's break that down by listing potentially applicable definitions of that word.
- PERMIT
- to fail to restrain or prevent
- to give an opportunity : PERMIT
A word in all caps means it is referencing another word to give context/explain a given meaning. So, we dig into the word "permit".
- to consent to expressly or formally
- to give leave : AUTHORIZE
- to make possible
And finally, authorize.
- to endorse, empower, justify, or permit by or as if by some recognized or proper authority (such as custom, evidence, personal
right, or regulating power)
- to invest especially with legal authority : EMPOWER
(I excluded some definitions because they weren't applicable to the situation, in my opinion. I could give a breakdown of why for each, but the pedanticness of this answer is already more than this community generally tolerates.)
Nine interpretations
- you are immune to magic that permits other creatures to know your alignment
- you are immune to magic that fails to restrain or prevent other creatures to know your alignment
- you are immune to magic that gives an opportunity [for] other creatures to know your alignment
- you are immune to magic that expressly consents [for] other creatures to know your alignment
- you are immune to magic that gives leave [for] other creatures to know your alignment
- you are immune to magic that authorizes other creatures to know your alignment
- you are immune to magic that makes it possible [for] other creatures to know your alignment
- you are immune to magic that endorses, empowers, justifies, or permits via the proper authority other creatures to know your
alignment
- you are immune to magic that invests other creatures with the legal authority to know your alignment
(The authority of the last two refers, in this context, to the laws or god or goddess of magic's authority.)
So, there are up to 9 ways to interpret the wording of the rule. I make it a point to list all potentially relevant interpretations, as the disagreement on this question largely boils down to interpretation of what a word means.
That's a bit unwieldy to handle, and largely unnecessary, so let's see what we can reduce.
Thinning the results
We'll address definition 3 first, as it is invalid to use that definition in this context.
That particular definition of "allow" is an "intransitive" definition, meaning that there is no direct object.
In English grammar, a direct object is a word or phrase that receives
the action of the verb.
In this case, it is "creatures" that are receiving the action of the word "allow". Therefore, we cannot use definition 3, as that is the intransitive usage (see more on the dictionary's page, including examples of that definition to see why it doesn't apply.)
We can then throw out 1 and 6 as well, as "permit" and "authorize" are covered by their own definitions, so those can be handled by 4 and 7, and 8 and 9, respectively. Likewise 5 is covered by "authorize"'s definitions.
Numbers 8 and 9 are similar enough that we'll just use 9. Likewise, for something to consent it has to have the authority to give consent, so we can roll 4 into number 9 as well.
Finally, I reject definition 2 from applying to this situation, as that is the "How could you allow this to happen!?" definition. For that to be what was intended, it would mean that the default state of the universe was that creatures could the alignments of others, and that this ring prevented magic that did nothing to stop that. That doesn't make much sense to me.
Two unique interpretations
That leaves us with just two interpretations:
- you are immune to magic that makes it possible [for] other creatures to know your alignment
- you are immune to magic that invests other creatures with the legal authority to know your alignment
Interpretation: Make is possible
This is the definition that the indirect camp is using.
The ring makes the wearer immune magic which makes it possible for
other creatures to know the wearer's alignment.
Interpretation: Invest with legal authority
This is the definition that the direct camp is using.
The ring makes the wearer immune magic which invests other creatures
with the legal (magical) authority to know the wearer's alignment.
Conclusion
This brings me to the unsatisfying conclusion that both interpretations appear valid.
As such, it is up to the DM to decide how they want their campaign world to operate.
On the one hand, it makes sense, based on the name of the ring, that the wearer is shielded from all means of their alignment being detected.
On the other hand, it could create some very convoluted reasoning to describe how or why a hypothetical magic item doesn't react as it normally does, just to prevent the wearer's alignment from being able to be deduced.
Ultimately it is up for each DM to decide what works best for their table.
For those who are disappointed in this answer not resulting in a clear answer, you are not alone. I started it thinking it was going to lead me in a specific direction, but ultimately the definition of the word "allow" does appear to be ambiguous enough that either interpretation is valid. I don't want the effort to go to waste though, and I figure providing a basis for each interpretation is valuable to DMs in deciding on their own ruling. Or someone can poke a hole in one of the two interpretations and post their own definitive answer.