" I’m assuming a hole will have to be cut in the stud for the drain to go through but won’t that compromise the strength of the studs that are holding the carrier in place?"

Yes, but it doesn't matter. The stud only has to be strong enough to hold up drywall if the wall is properly framed.

I think you'll have to leave at least 1 1/2" of stud, even if you have to pull wall out away from brick. That installation in the last pic is sketchy. There's nothing to resist the torque on the carrier but drywall.

Seabornman - that was my thought as well. I think pulling the wall a bit away from the brick makes sense.

Most of the weight is initially straight down, so the metal frame that goes down to the bottom plate will take that load. However, as soon as someone sits down it will make the metal frame want to rotate forward, which means the upper horizontal section must be able to hold a lot of weight.

A typical 180-200 lb person sitting on a toilet that extends out about 18"-20" needs a lot of support to that frame to keep it vertical. The one in the 2nd picture looks unlikely to be enough to hold the weight, since the top horizontal blocking is not attached to full vertical studs on both sides like it is in the first picture.

Bruce

I know it's been four years, but I've been thinking about this. There are 4" penetrations in both pictures. The last one is a notch, the former is presumanly a hole that you can't see due to the angle.

The carrier frame is very stiff and is longer than the toilet seat, so it spreads out the pullout force. It's also attached to the upper stud in two places on each side, so it's trying to pull the rotate the entire stud forward, which is attached to the top plate, so isn't moving. I'm reasonably convinced that even if 2x6 is severed completely (below the horizontal attachment screws, it would still hold 100s of lbs on the lip of the toilet without issue. If anybody has experience otherwise, please share!