I do not use a fanny pack or money belt. If you do have a money belt, it should never be accessed in public.
I avoid the deer-in-the-headlights look. Even if I have no idea where I am, I'll continue to act as if I know where I'm going, either occasionally checking the phone map or asking directions if necessary.
Those two bits are the big ones. Pickpockets and scam artists can smell fear and naiveté a mile away.
You can NOT avoid looking like a tourist in some situations. If you're pasty white and in the Marrakesh medina, they'll make you as a tourist.
I won't touch a selfie stick with a 10 foot selfie stick. If I carry a camera other than my phone, it's a small micro-four-thirds mirrorless one.
Some logistical / packing decisions I've made:
I've pared down my luggage over the last couple of years, after constantly bringing home half of what I took unused. Last few 1-2 week trips have been done with a 13 liter Osprey day-lite pack. I've standardized on mostly merino wool layers. How does this make me look less like a tourist? My pack is the same one I usually use as a daily-carry laptop bag. If I can fit into a coffee shop at home, I can fit in elsewhere.
I prefer pockets with discreet zippers. Cargo pockets are also very touristy, but I still prefer them just to carry a hat, sunglasses, etc. Passport in the front left pocket where I would normally carry my keys, couple of cards in left rear, small amount of cash right rear, backup cards some other pocket, phone in right front pocket. These are standard for me - keeps me from forgetting one or more items if everything has a standard pocket. Nothing goes in jacket pockets, because those can get left behind.