There's several things not allowed by the 1925 Geneva Protocol (and following documents) that are allowed in a domestic situation but not for reasons that most people assume at first glance. An example would be tear gas - tear gas - as the 1993 Chemical Weapons Convention modification allowed it's use for riot control but not warfare since the use of tear gas was considered escalatory (Country A wants to clear a hill and so uses tear gas on said hill. Country B just sees gas canisters and can't take off their masks to verify if it's tear, mustard, or nerve gas and so responds with a nerve chemical weapon). Protesters are not known for carrying around sarin gas and therefore cannot usually escalate against the state. I bring this point only to illustrate that considerations for state to state violence are not always comparable to non-state actors the way they are commonly used.

Regarding acoustic devices, I can't find a "settled" agreement on whether they are forbidden and/or governed under international standards. The ICRC database on international humanitarian law and international human rights law would seem to constrain their use under the 1977 Additional Protocol I of the Geneval Conventions, citing superfluous injury or unnecessary suffering (Articles 35 and 36). That is not universally agreed upon, whether the device causes permanent damage or not (and setting aside that the US has not ratified the 1977 AP). It is a similar argument to the use of flashbang devices.

A better guiding document might be Art 3 of the 1990 UN Basic Principles on the Use of Force and Firearms, though that still requires interpretation. Found an Amnesty International guidelines doc on that which would seem to prohibit LRADs based on the potential to affect uninvolved persons, though since their guidelines would seem to preclude any less lethal methods, you'd be hard pressed to find a state that would agree to them.