Businesses have a right to decline credit card purchases even if they accept them. It's just rare a business will stop someone. But you do see signs sometimes saying if you want to use a credit card you need to buy $10 or $20.
Businesses get charged a fee from MC or Visa. I think the general estimate is 3%, so it's a direct hit to their bottom line.
Points cards typically pay you back about 1-2% worth of your purchases in the form of store points or dividend pay back. I prefer my boring credit card that is no annual fee and pays me back 1% on all purchases, with some things like food and gas at 3%. I get a $50 cheque in the mail about 3 times a year. I'd rather have that then be forced to use it a store.
I wouldn't worry about stores getting dinged 3%. It's business. They make plenty of margin on products they sell. And credit cards make it easy for people to buy stuff as opposed to keeping a mound of cash in their wallet. Also, most people carry credit cards tied to a store, so a person will be spending that money back there soon. Repeat business.
If possible, always use a credit card as even basic ones give you consumer protection. And you don't have to pay it for a month. It also helps build your credit rating. As long as you have control over your spending and don't go wild buying stuff you can't pay off, always go credit card. Debit is for suckers unless someone totally and completely can't control their spending and has to pay off stuff as they go.
I've done my share of calling them to fight a charge. And I''ve won each time. They did the fighting for me and next thing you know that charge is reversed on my invoice. They don't even contact me telling me they won it for me. It just showed up as a reversal. Debit cards give zero protection as the money is immediately deducted from your bank account so have fun trying to claw back any improper charges. If it's a large store not a big deal as they'll likely give in, but if you are trying to fight debit charges from no-name places or sketchy repairman you'll be fighting it forever.
Some basic cards even give you travel insurance and extended warranty protection for free too. You just have to read up on all the benefits. No annual free cards give you less perks.
If you feel comfortable wheeling and dealing, I've done my share of paying cash instead of credit card with the business negating tax (trusted repairman I know for years). It's a risk from my part as I might get a crap product but I've never been burned. In return they save credit card fees and pocket the money.