Nooooooooooooooooooooooooooooooooo! Not tap shoes!!!!!

Any recommendations???

High boots, with laces, are likely best. Between havin to walk through Missouri clay (SUPER sticky mud!) and, inside of the caves, a combination of bat guano and clay mud (stinky, sticky, yucky, yuck!) the best I had was very high laced boots. Lace them good and tight (don't cut off your circulation though!) and wax them plenty. I use shoe polish and really wax them good. I've seen some do hip waders but I was never sure if that was best or not. Never tried them myself.

Reason I said "Noooooo...." was I love to tap dance. It'd be like a musician seeing someone using a great guitar as an oar to row their boat. LOL

Ooh, boots, I've tried boots before, tall with laces, and its not for me, though they were fabric and tended to collect mud vs slide through it. They made things exceptionally difficult for me, as the more I walked the more coats of mud were applied until I could barely lift my legs from the muck due to weight alone, it nearly imobilized me where I stood. I had to wipe the ample layers off before I could continue, and repeat the wipe down every few steps otherwise i'd get stuck fast in the muck. It was a very challenging experience.

I tried again with a MUCK boot which is designed for farm use, and had some better result, though those winded up being too heavy, and bulky to really be viable for my use.

Yeah. Cloth anything doesn't work. Might be light weight but mud/muck clings to it like a tick to the scalp. Leather tall boots (the lace up type, not the open top... never use anything that has an open top!) are my go to. Yeah... they can get a bit heavy but good one's are fairly lightweight. You don't have to get the super tall... those that lace up to just below the knee... but they do work best. Next would be military style boots. Not the surplus heavy leather ones but the lighter weight jump boots. And there is a trick I use that can help... apply a very thick layer of boot wax polish then go over that with a hair dryer. Set it so you can see the polish barely melt (usually low or medium setting) and go over the whole boot with it. Then wipe down and do it again. Re-apply one more time and repeat the process. Finish with a proper polish (shine) and stuff will slide off easier. Leather is porous enough that the wax can sink inside the leather a bit and that way it waterproofs better as well as lasts longer. Learned that trick in the Army.

I might try this next season or something. Personally I’m quite fond of the level of control that I have in my shoe choice. A mary-jane style especially the tie-on type stay on the feet and are slick to the mud. I have some heels (also dance, not tap) shoes that rightly apply to my feet where I never feel like I’m going to slip from them

In the end, it actually depends on what you're stepping into more-so than the shoes you wear. I mean, I've stepped into stuff that threatened to tear my leg off... took 4 people to work together to pull me out. When the muck/mud is that bad... that sticky... it literally forms a suction that will rip off shoes, socks, and you'll swear you leg is next. It can even hurt sometimes trying to get extracted. When it's that bad... it's actually best to go naked (legs... not body)... at least from the knees down. And some vasoline doesn't hurt either.
Normal muck/mud isn't as bad so tap shoes or boots aren't terrible. The slicker the surface of your footwear, the better. Also, as I said, stay away... far away from anything with an open top. Have fun in the muck!

I love to tap dance too! So fun and great exercise!