Damned if you do, damned if you don't.
For example, Target in the US gives you 5% off for using ACH (which debits your bank account).
But other retailers, like Walmart and Home Depot, are betting that people spend more if they use a credit card to buy.
That's out of date. Since 2013 merchants have been able to surcharge for using credit cards since 2013 (except in places where it is illegal). Here's a Q&A from Visa about this [1].
There are five states (Colorado, Connecticut, Kansas, Maine and Massachusetts) where state law makes credit card surcharges illegal.
Even before that they could effectively surcharge by offering a discount for not using a credit card. (That also works in the states that ban surcharges).
[1] https://usa.visa.com/dam/VCOM/download/merchants/surcharging...
In the US, credit card companies charge 2.5% - 3% merchant fees on every swipe, and their agreements forbid merchants from passing these costs on to customers. The net result is that merchants raise their prices for everyone to cover the cost of the credit card fees. Essentially, even if you're paying in cash currency, you're still paying a sales tax to the credit card companies.
The only way you can avoid this tax is with a lucrative rewards card. Anything else you do -- pay by debit card, check, cash -- will result in you paying a sales tax to the credit card industry.