I'm in the "happily wear the money belt" group. My husband is in the "I hate it but I'll wear the money belt anyway" group. Neither of us tucks in a top/shirt of any kind, so getting to our money belts is easy -- for us. We put our passports, driver licenses, emergency info including meds lists, credit cards, debit cards and "big" money in our money belts. Even with all that, they are still very thin and flat and not at all noticeable on us. We rarely stay anywhere that has a safe, but if we do, it gets other things like "really big" money, his iPad and my jewelry put in it.
This may be TMI, but this is how I wear mine. I always wear a tight shapewear camisole for the most obvious reason, but also because it helps with my posture and supports my back. Most people don't realize that with shapewear that goes down lower than your waist and over your hips, you are supposed to pull your panties up over it, not wear them under it, even though it is usually shown online with the panties under it. So skin out on the bottom, I have shapewear, money belt, panties, pants.
The money belt never touches my skin. I wear it in front because it is easy to pull out when needed, especially since the shapewear is slick. My pants either have a stretchy waist or are big enough that I can pull them and the panties out front enough for easy access. My husband wears his money belt between his shorts and pants, so it also never touches his skin. In either case, we would really have to be in a bad way for anyone to get to our money belts without us knowing it.
For our last trip, I got a neck wallet on a string. I took it on the trip and used it to store the currency I wasn't working in at the location. It ended up locked in the safe or my luggage. After several attempts at home and a couple on the trip, I couldn't for the life of me figure out how to wear it comfortably. I couldn't tolerate it under the shapewear, and over it meant it was between the shapewear and top. I think they may work for men or for women less curvy than I am, but it was always on the dark side of the moon(s) on me and the string strap really was annoying. I even tried putting it around my waist and inside my pants, but it was too bulky and big for that.
I much prefer the money belt, but I might try pinning a hidden pocket/belt loop style in my pants sometime. It might work with some of my pants, although probably not those pull-up ponte knit ones that I love so much for traveling!
BTW, has anyone noticed how many pictures there are showing money belts or neck wallets being worn on the outside of people's clothes? No wonder people get it wrong!