You cannot contract out this provision.

Suppose I'm a customer of your employer, and my contract says that the payments due are $1,000 per month by cheque or bank transfer only. I try sending $1,000 cash. Your employer rejects this payment and asks me to pay by cheque or bank transfer, per the terms of the contract. If I refuse, I'm in breach of contract and that gives your employer the right to foreclose on the lien against my house (subject to relevant local law and contract terms).

However, by breaching the contract, that also means I owe your employer a debt equal to the amount of the payment (or more, up to the entire amount, again depending on the exact terms and applicable law). If no money is owed, then your employer does not have the ability to foreclose. They can take me to court in a foreclosure action, but if I then plop down a stack of $100 notes of the correct size, then that absolves the debt. In reality, if this happened, it's probably more likely that the judge would direct me to pay the court clerk and have the clerk write a cheque or tell me to buy a cashier's cheque.

If they specifically want payment by bank transfer or cheque when they sue me, they're not suing for damages; they're suing for specific performance. That's not easy and it's usually quite hard to justify to the court why you want specific performance instead of just damages, especially since this would be a pretty facetious case to begin with. At the same time, I do think there is a good chance the judge will say "So the defendant offered the full amount that you want in cash and you turned them down? GTFO of here, case dismissed."

The act of offering legal tender as payment for a debt absolves the debt. If I offer your employer payment in cash, they cannot point to the contract as an excuse to refuse.

If you can cite case law to the contrary, I'm happy to admit you're right and revise my comments.

So no, businesses in the US do not have the "right to contract" out the legal tender nature of cash. It's just a small thing called "reality" that prevents the situation I describe from actually happening.

1. People are usually not stupid enough to play games and test the limits of the law with their mortgages and houses.
2. Being unreasonable is a great way to get judges to hate you and assess costs against you. Nobody is pretending that refusing to pay with a cheque or bank transfer and then bringing a briefcase of Benjamins into court when the mortgage company tries to foreclose is reasonable.
3. There is literally no benefit (to sane law-abiding citizens) to insisting on paying cash when paying by cheque or bank transfer creates a verifiable record of payment and orders more convenient and is much safer than sending large quantities of cash by post.

So is this conversation almost entirely pointless? Yes.