Many of the tips I see for cleaning BP guns recommend removing the barrel from the receiverfor convenience of cleaning. I am wondering tho, if you have a scoped gun, would removing and replacing the barrel from the receiver, possibly slightly change your sight picture and maybe alter the POI of the weapon? Or would the effect be so small as to be negligible? I'm guessing that if you were careful to use the same force in tightening the receiver screw that it would be negligible.

Any thoughts?

In my experience - negligible.

I don't remove my barrel for cleaning, just never seen the need...

I usually remove the scope (QD rings) and take the actionout of the stock, or barrel off the receiver on a break-open action. Just takes a few seconds, and makes cleaning easier.
No change in POA/POI.

It all depends on the make of rifle. A pinned barrel I never remove. A wedged barrel, why not. And one held in by lug locking screws I always do. If I put that barrelback in the stock and the rifle shifts POA then I am guessing that a bedding job needs to be done. I have been removing them for years I never noticed a problem.

It just makes the barrels and parts easier for me to clean the way I do. All scopes are with Warne QD rings, so the scopes come right off. Then after I get the barrel and parts away from the stock I can use a water bath to get the main filth off everything and then just a few solution swabs, and then some dry ones and I am ready to oil the rifle up, check all the parts including the trigger assemble for fowling build up (which is kind of hard if you do not pull the stock.), and then get everything oiled, wiped down and back together.

The type and even the brand and model make all the differance so does what powder you use, my System One and my Hawkens have to be taken down and have the action cleaned every time,the Omega I take part way down, the Triumph I get absolutly no blow back on and I only clean the barrel and the breach plug on, I understand that the 25APC conversions are that way to. Lee

IMHO it depends on the gun design and I can speak only for the Remington 700ML (sold it to my friend) and current SS Omega with camo thumbhole stock.
I use to remove Remington’s barrel only after the end of hunting season to give an overall cleaning. Did not see any change of POI next year.
It is more difficult to clean the trigger group on Omega, so I remove the barrel after every trip on the range, but I use adjustable torque screwdriver ($60.00 invested) with 25 in/lb settings to tight stock screws. No change of POI at all.