Why did our cats stop using their litterbox and start pissing and shitting in our bathtub?

They're angry with you about something so this is their way of getting back at you. Until you find out why, how's this for a solution: keep the bathroom door closed.

Your cat sees you do it so it is mimicking its favorite person. 

Did you clean their litter box? If they don't find it clean ,they will do so

I have heard that stress can cause a cat to not use it's litter box. If the cat was using the litter box before, there could be something that has changed in the house. Did you bring another animal into the house or did you change anything in the house, add something new, remodel, put something in the area of the litter box, even introduce a different smell or scent? Cats usually don't like things to change and will investigate things that are different or changed in the house. It also can be a health problem with the cat and you should ask your vet about it, they would have some answers to what may be causing the problem. Good Luck in finding out what is causing your cat to change.

Did you clean their litter box? My cats are like dogs they go outside.

My cat does not have a litter box.  She won't have any part of one.  She is trained to meow at the door to go out and she will wake you up in the middle of the night if she has to go.  She's very good and consistent about it too.  There was one time when nobody was home and she had to go, so she did what I consider is the smart thing in such an emergency and went in the shower to pee. MUCH easier to clean up.  A dog would have gone all over the carpet.

Some possibilities:

Litter box is filthy and needs to be cleaned or changed

Cats don't like the litter you're using

There's a power struggle between them that is preventing them from using the litter box

Location of the litter box. Most cats don't like their litter boxes being near their food or the box is in a place that makes them uncomfortable

Type of litter box being used. Some cats freak out over the self cleaning models because of the noise

Check to see if any of these are a problem with your cats.

Maybe it is the litter you are using. Whenever my boyfriend would buy the wrong brand of litter my cat Atticus would use the tub. He would only use Dr Elsey;'s or Frisco Cat Litter from Chewy's. Some cat litters may have sharp pebbles and Dr Elsey's is more of a medium grade litter in softness to the cat's paws. Get a bag of Dr Elsey's Cat Attract this may solve the problem. We also kept our bathtub filled with a special magical litter (water)  whenever Atticus would jump in the tub he would jump out as soon as he noticed it..

Your litter box must be filthy nasty dirty. And you can cure your cat of using your bathtub fill it halfway with cold water and Toss your cat in add a teaspoon or so of mint flavoring the kind that you use to bake a cake with.

If the cat repeats the ACT fill the tub up again and throw him in again.  It won't take very long before your cat understands that a tub is where it gets wet each and every time.

Feeling the need to urinate on a cold surface may indicate a urinary infection.