I don't see the issue. I grew up surrounded by this as a USAF brat, including in Germany in the 70's when Ulrike Meinhof was still at large and Andreas Baader was locked up nearby - I felt much safer from the Red Army Faction when I saw people with automatic rifles in the uniform of my country outside the BX. When I see a Mexican Marine or QR state police officer with a weapon in clear sight it similarly gives me a sense of reassurance that they're watching out for me, my neighbors, and visitors.
I do not see any reason why civilians need military-style weapons, but I have no problem whatsoever with properly-trained military and law enforcement personnel carrying such weapons. I have literally never seen one "brandished" by anyone other than a civilian, and only ever in the US.
Want to see some heavy firepower? Have a look at what's being toted around Heathrow by polite young women in police uniforms. Would you avoid going to England because their airport security personnel are very heavily-armed?