I had an older gelding choke twice on beet pulp shreds. The first time I had taken a short cut and fed the beet pulp dry mixed with senior. Now, I'd never seen a choke, and didn't really know what it was, and by the time the vet got there he just treated it as a colic, which it was by then.
The next time the gelding choked I had just wetted the shreds and not soaked them. After that I knew what I was dealing with and won't feed it without soaking it ever again. Choke is not a pretty thing to see.
The old gelding had his teeth taken care of regularly, he could still eat hay and grass fine, and he was not a bolter. He never had a problem again after I made sure the stuff was soaked.
If you can spread the shredded beet pulp very fine, like say in a feeding trough, I think it would be ok. But I think any time they can actually get a mouthful of the stuff it's dangerous.