I'd say it depends on a couple of factors...

First and foremost: Do you already have a buyer and did they already ask you about the washer/dryer? If so, and really this probably goes without saying, but if you already intoned that they can have it, then you need to be stand up and let it go with the house.

Secondly; it depends on how well-off you are financially. You don't have to answer here, but you should at least consider it privately. I'm not saying you should donate it to the next people in your house. I'm saying that if you can't easily afford a new one, then you should keep the old set. You will have plenty of unforeseen costs in the new build, and for most of us that means debt. Keeping the old set could give you a few more years to allocate approx. $1500.

I'm sure you know that they don't make them like that anymore.

Whether or not to bring them all comes down to what type of washer you want in your new build. If you prefer the traditional top load agitator type, you like how your Whirlpools perform, and you aren't averse to repairing rather than replacing if they break, I would absolutely bring them with you. You won't be able to find a true equivalent to them being made today, and the only one that's comparable in quality (Speed Queen) you will be paying through the nose for, both to buy it initially, and if it breaks down the road. Since there were so many Whirlpool direct drives made over the years, parts for them are easy to find, not too expensive and everyone knows how to work on them. They are a super easy to work on design, if you're the DIY type.

If, however, you are thinking about making the switch to a high efficiency front load washer - no time like the present. I did it almost 20 years ago and haven't looked back.