I'm not aware of any federal exemptions to gun laws for military/ex-military citizens.
The only ones I've seen relate to state gun law in e.g. AZ, where if military/ex-military want a conceal carry permit, the training requirement is waived. You still have to submit an application with fingerprints and everything to DPS. (Which is kinda moot anyway, since AZ citizens who can federally own a firearm can also open/conceal carry.)
I'm not aware of any federal exemptions to gun laws for military/ex-military citizens.
The only ones I've seen relate to state gun law in e.g. AZ, where if military/ex-military want a conceal carry permit, the training requirement is waived. You still have to submit an application with fingerprints and everything to DPS. (Which is kinda moot anyway, since AZ citizens who can federally own a firearm can also open/conceal carry.)
Illinois recent AWB has carveouts for police.
https://dd214direct.com/veteran-need-guncc-permit/ has some additional details, but largely agrees with you; some states also lower the age requirement for veterans.
Louisiana recently passed a law allowing vets to concealed carry without a license https://www.audacy.com/wwl/news/local/concealed-carry-law-could-be-model-for-other-states , but this definitely seems like the exception and not the rule