You are correct that, while unlawful combatants are not guaranteed the same rights under the Geneva Conventions as lawful combatants, there is no requirement to actively deny those rights. However, there are some very good reasons for going out of your way to not treat unlawful combatants as well as lawful combatants. As you mentioned, not everybody is a signatory to the Geneva Conventions. However, a lot of countries/groups that aren't signatories, have made varying levels of effort to abide by them anyway in past conflicts. This is generally a good thing. There are two main incentives for non-signatories to try to abide by the Geneva Conventions: first, if they lose, they are less likely to be subjected to war-crimes trials at the end of the conflict; second, if they are captured during the conflict, they will enjoy the status of lawful combatants. If they know that captured unlawful combatants are given the same treatment as captured lawful combatants, they will have much less incentive to abide by the Geneva Conventions. Therefore, it is a good idea for Geneva Conventions signatories to not apply the full rights of lawful combatants to captured unlawful combatants.

Incidentally, the Geneva Conventions do provide some protections for unlawful combatants, just not the full set of protections guaranteed to lawful combatants. You can't just shoot them out of hand. However, you can put them on trial, sentence them to death, and execute them. The Geneva Conventions don't really spell out due process requirements for such situations, so the distinction between "shot out of hand" and "executed after trial" could potentially be trivial.

>So when a non-state organization takes action against a state, this makes it legal for the state to treat them however they want.

This is not true. If the non-state organization abides by the Geneva Conventions, and if the state they are fighting against is a signatory, then the state must treat the non-state actors as lawful combatants (depending on its scope and scale, a civil war could be an exception because the rebels could be considered traitors and tried as such). Even if the non-state actors don't play by the rules, they still get some protections, as I explain in my previous paragraph. The rules are actually quite easy to comply with, so smaller powers and non-state organizations are not "excluded" by an inability to follow the rules, only by a conscious choice to break them. For example, something as simple as color-coded armbands will satisfy the requirement to wear identifying insignia.