Is there supposed to be tension on the sling when you hold a weapon using the typical C-clamp method?
There is no right or wrong
The C clamp hold can be with or without sling, it’s about stability and control of the barrel tip
Slings can just about carrying to ease the load and to allow you to free your hands - in which case it doesn’t matter how tight or loose it is, just that it holds in a manner that you can get back to it.
Slings can also be about another point of contact for stability and therefore need some tension. If you have some tension in the sling then this almost counts as being ‘attached’ in a ‘fixed’ position:
The combined tension between the sling pulling back to your body, stock against your shoulder and you forearm pulling away gives three points of ‘contact’ steadying the rifle in the direction that you point
If it works for you then it’s right - but with the issue of reloads
@Wavey_Gravey has it - release the tension by dropping the stock from your shoulder.
Consider how flappy the rifle is when hung from the sling to pop your pistol out - if it’s just an emergency couple of shots then it doesn’t matter too much, but if you switch to pistol and carry on with pistol then a flappy rifle is very annoying
What works for you works for you
So if there’s a problem effecting you then focus on resolving the problem, if there are others saying that you have it wrong then that’s their problem