This looks like what is known as a "Tanga" thong. A typical thong has just the one string that runs down the butt, but a Tanga thong is meant to partially cover the upper portion of the buttocks for slightly more coverage. The cheeks are meant to hang out from underneath this type of underwear as opposed to a fully covered style.
Not quite sure what the safety concern is. Your privates do need breathable material to rest upon and some underwear isn't, but this is only a problem if you intend to wear those materials in an underwear say on a daily basis. Every once in a while isn't an issue.