Pretty much that, and various other things guests carry - Disney knows there are a lot of people carrying bags, coolers, drink bottles, camera bags, purses, and so on. And it's really only the 'action' rides where it matters - on slower rides the bag can sit between your feet in the ride car or seat beside you if there's room. Some rides like Big Thunder Mountain have small pouches that don't fit larger camera bags, but if you wrap the shoulder strap around your knee and stick the bag between your feet on the floor, it won't go anywhere. And as mentioned, some rides like Kali offer lockers to store bags you don't want to bring with you - as even the ride pouch areas provided on the raft are made for smaller items, and often end up getting wet inside anyway.
I tend to store my larger bags in a locker if I know I'll be hitting lots of action rides, and bring my camera with me with one chosen lens to shoot on-ride photos.
I've never had any issues bringing cameras on even the fast rides, as long as you can show you're taking good precautions...I tightly wrap the straps around my wrist multiple times and keep a good grip on it, and will bring the camera along on roller coasters and such as it's fun and challenging to try to get some shots while riding. I've convinced some ride operators that the camera was safer on the ride than people shooting with phones, as they have no straps holding things to their body in case their grip gives out - my camera will stay on my wrist while someone's phone could go sailing into someone else or fly free into the ride tracks.
Tripods are OK in all the Disney parks as long as they're not giant ones...you may have trouble entering with some pods that are more than 21" when compacted - though I've had some fellow photogs manage to get in with those strapped to their camera backpacks - it's just a matter of luck and taking the chance. Better if you have a reasonable pod that can compact down - aluminum 3 or 4 leg section pods that are less than 21" folded are fine - I've brought my Slik pods that extend up 65" and can handle pretty decent weighted lenses and never had an issue. The good thing is those tripods will fit in the standard Disney lockers that you can rent at every park entrance...so if planning on using it later at night and not wanting to haul it around all day - rent a locker, stick the pod in there, enjoy your day, then when ready, retrieve the pod and enjoy the long-exposure night shots.