I have always used glass jars, crocks, etc. but found a nice plastic tub....will this work okay?
I ferment in plastic tupperware all the time. As long as it's a food-safe plastic (BPA free is what you want I think), you should be fine. That said, if it's just the one tub, I'm not sure it's worth it, unless you devote an entire shelf of your fridge to kraut and the tub fits perfectly. (And even then I'd recommend getting a set of smaller, stackable containers instead. That way you could take one out at a time and not disturb/introduce outside air to the rest of your kraut.) Here are some things I know about fermenting in plastic tupperware. I hope you like text.
One is that you will likely never be able to use that tub for anything else again, ever, unless you're okay with whatever else you put in it smelling like kraut. One time I whipped some cream in a tupperware I had stored kimchi in. That was a mistake. (That said, you get a really interesting texture if you fold whipped cream into egg and scramble it.) Seriously, I scrubbed with baking soda, dish soap, clorox, hydrogen peroxide, rubbing alcohol, and everything else I could think of afterwards just to see if I could remove the smell. I couldn't.
Two is that you might need to seriously reinforce the seal of the lid. Most plastic containers don't have a true airtight seal or airlock. You could have issues with contaminants down the way that you don't need to worry about as much with glass crocks designed for fermentation. You can fill your tub with water and tip it over to see how well it holds liquid, but that still won't tell you about air.
I only ferment kimchi in plastic because, hey, I can't use those tupperware for anything else now, and the brine also dissolves flour, kills yeast, and likely strips paint. It's powerful. But even so, I don't leave it at room temperature once it stops actively fermenting. Kraut is not as crazily strong as kimchi, in my experience, so I'd be even more careful about storage conditions if you use a plastic tub with a non-airtight seal. Even if the acidity of the brine should protect it, better safe than sorry.
Two and a half is never EVER travel with a plastic tub of fermented goodness that is NOT double-bagged, at least. Double-bagged in a cooler is better.
Three is to consider where you'll put the tub, physically. Will it fit in your fridge, and can you pack effectively around it? If you don't do cold-storage, or have a fermentation fridge, I'd honestly reconsider changing your container drastically to anything, especially a plastic tub not designed for it. If your current method ain't broke, don't fix it.
Four is that fermenting in plastic leads to a less-pretty presentation. I can use a bright red, bubbling jar of kimchi as a centerpiece at dinner if I want to. Or just tie a ribbon around the rim and say "Merry Christmas!" Sauerkraut looks cool too. So do pickles, if I break my fingers arranging them in the jar. The plastic tub, possibly wrapped up in grocery or trash bags, really doesn't have the same effect. Same delicious product, but the tub cannot be used for decoration. Plastic just lacks that kind of charisma.
So, again, yes, you can ferment in food-safe plastic, and it's cheap and great for cold-storage in a fridge because it stacks easily, but I would definitely take a good look at the seal, and think about your typical storage practices. I love my tupperware-kimchi and have no issues with it, but that stuff is nearly indestructible. Even with all my positive experiences using plastic for kimchi, my other ferments, such as kraut, dill pickles, carrots, squash, onions, garlic, okra... all get glass jars, just to be safe.
I think it would work, although I would suggest to stick to glass as you've been doing in order to avoid any leakage from the plastic due to possible temperature changes, UV exposure and as a general better option. Have a wonderful day.