No, It will cause issues later in life. Whether or not little girls and little boys start out the same, They will eventually grow up and change and become different. The genders are equal, And girls not being allowed to go topless is not a sign of gender inequality. Teaching little girls that wearing shirts makes them lesser is simply wrong and could cause issues later in life.
It's nothing to worry about (if you're a good guy) 1. Inside threats (shootings, Blowing up stuff, Spies, Etc) are hidden amongst the citizen population.
2. Which is more important? Privacy or safety? If your office building is being blown up are you going to be worrying about your Instagram photos or that one call you made to ask your roommate to take out the trash?
3. If you're not doing anything illegal, You have nothing to fear.