Just to chime in, in case I and the OP are part of your "they" (bold added), I was most
definitely saying you should not be able to sneak attack with a rapier... but that's because I, personally, don't feel rapiers belong in a D&D setting. Otherwise, yet, I am definitely saying other weapons , which are smaller, lighter, etc. should be able to sneak attack.
I know the 5E term is not the same as it used to be. Back in AD&D when it was "back stab" it really did more mean an attack by surprise. Now it is just a "find a weakness, etc." as
@Greenstone.Walker says. I know they did it so rogues could keep pace with other battlers, but IMO not everyone needs to be able to keep pace with everyone else in their strengths.