First, I don’t see the constitutional argument that allowing certain people, based on their employment for the government, to be exempt from laws outside of their employment.
From a philosophical standpoint, that is indeed very troubling. There is however a very powerful counter-argument: Law enforcement is on duty 24x7. That's actually not just the law, and also not a joke, talk to some officers sometime: It's not unusual for their radio to go off at 1am, when they are off shift, and get a request: "please come in right now, we need more help". This is particularly true in remote areas, and for certain types of LE that are spread thinly. Example: State park rangers (who are full LE with badge and gun) in the remote parts of the Northern California coast or the Sierra foothills. There is a reason friends in those careers always keep their uniform pants and jacket, and their duty belt (with badge, gun and radio) ready to go on at a moment's notice.
Another example (from a friend) who works in a big city PD (as an undercover investigator mostly): Going out to dinner with spouse and kids, and someone recognizes them and smiles and waves. Turns out the someone is a person our friend helped put behind bars for several years. Fortunately, the someone was friendly this time. But there is a good reason our friend always carries when off shift; you never know when the next someone will not be friendly.
Secondly, also disagree the government employees should be exempt on duty as well, but that’s a harder argument because were are so accustomed with that being the case.
That argument won't fly. On duty, as part of police and public safety work, agencies are allowed to do things others are not. For example: Go way over the speed limit, make U-turns in the middle of the freeway, have a rifle or shotgun loaded and in plain view in your car, and so on. And that includes things like large capacity magazines or off-roster guns. Part of that is being better armed than their opponents. From a hardware and equipment viewpoint, there is a similarity with the military, which is also allowed things that normal people don't have access to.
One could take the viewpoint (which is somewhat hinted at in the prefatory clause of the 2A) that both law enforcement and military are identical with "the militia", and one could then define the militia as "all able-bodied people (or males?) between the age of X and Y". That viewpoint was popular 300 and 250 years ago, and remnants of it exist in anarchist communities. For our society at large, this viewpoint is not relevant any longer.
I think these exemptions are partly attempts to maintain LE union support for these laws.
That trope is always used to explain why democrats (supposedly always in bed with unions) like to exempt LE from gun control law. And theoretically it might be true; after all our democratic politicians involve some unions heavily in decisions. BUT: They do that for a reason, namely delivering votes (not so much D versus R, but more turnout). And that argument only works for large unions, first and foremost the CTA and the SEIU where it represents government employees, and also large construction trade unions. The LE unions in California are fragmented, and always at each other's throat (there is nothing a park ranger hates more than a Chippie, and the feeling is mutual). And most LE are not actually reliable D voters anyway, independent of how much their unions play along with politics in press releases. I don't think buying off LE unions with gun law exemptions works, and I know democratic legislators share my viewpoint.
What does work: Appointing roughly half of the State Board of Education to be CTA members and lobbyists. That nets a governor a quarter million reliable votes. Or a school board pay the highest paid teachers even more, again the CTA will handsomely reward them at the next election (and young low-paid teachers get kicked to the curb, because the CTA doesn't care about them). Or require certain construction projects to only use unionized workers. In my (not at all humble) opinion, the CTA is the most evil thing in California politics, and responsible for many of the ills of our school system. But they get reimbursed handsomely for their power.