if you had your window shade down you wouldn't even notice it
You wouldn't notice a change in apparent gravity, but you would (at least I would) notice the angular acceleration, like when entering or exiting a banked turn.
My (very non expert) understanding is that this would be a weaker feeling than many you get on a plane, and not rise to the level of conscious perception.
There's lots of things we could do, but don't. Generally, the risk/cost is non-zero, even if small, and the recognizable value (that which can be captured or benefit to the decision-maker) is less than that.
I'd probably pay a little bit to see this in the skies while I'm safely on the ground, and even to be in one after the first 10,000 have gone by. But I wouldn't pay enough to make up for the lawsuits and loss of revenue from people who don't like the idea.
Here's Tex Johnston talking about the manuever.
"What do you think you were doing up there?"
"I was selling airplanes"
While the president of Boeing was allegedly quite upset, Eddie Rickenbacker, the head of Eastern Airlines, was a WW1 flying ace and allegedly said "You slow-rollin' S.O.B. Why didn't you let me know? I would have been riding the jump seat". So the manuever may indeed have sold some airplanes.
Very few people have been on a plane performing a barrel roll, but we could fix this. Commercial aircraft could roll in revenue service, and if you had your window shade down you wouldn't even notice it.
While there are many ways to roll an airplane that would cause complete havoc inside the cabin, a barrel roll can be performed as a "1g" maneuver. With careful control of the aircraft, the forces can be balanced so that you only ever feel close to 1g of apparent gravity, and it always is pulling you down into your seat.
This was famously completed by Tex Johnston, without authorization, in a prototype Boeing 707. As acrobatic maneuvers go it's very safe, because the stresses on the airframe are minimal. We could update the programming on any modern airliner to allow the pilot to trigger a barrel roll, and it could smoothly move the plane through the whole process.
A major reason we wouldn't do that today is it's not worth it for the manufacturer: it would be a lot of work to ensure the code was completely correct. I wonder if as programming, validation, and evaluation continue to get more automated the cost of adding this and getting it through regulatory approval would get low enough that we might see some airlines use this in marketing?