Both gas and groceries are competitive in the places we've shopped. Of course that varies week to week so we don't shop there exclusively.  Where we winter the choices are Safeway, Fry's and Walmart. Walmart is clear across town.

Their "Membership" is free so why would that be different? Walmart offered us a credit card that would give us 3% off when used in their stores but when we applied they didn't like our address. We shop there too when it suits us.

I'm not familiar with HEB? 

BnB

HEB are big in Texas.   Most of them are nice stores.   Would shop there is they were in the Phoenix area.   

We use Safeway and Fry's (Kroger) because of the ability to get fuel discounts.  Especially at Safeway, I've been able to get $1/gallon off several times by using their loyalty program.   Now, with our hybrid, we don't use as much fuel, but every little bit helps.  

  On 9/27/2019 at 10:25 PM, scouserl41 said:

Walmart offered us a credit card that would give us 3% off when used in their stores but when we applied they didn't like our address.

I got a Walmart credit card because it offered a $25 credit on my first statement, and I happened to be making a $25 purchase with another CC.  The cashier offered it pre-approved and would place that purchase on it.  So I got that merchandise for free.

When the permanent card arrived, the terms changed to 3% off orders placed on their website and 1% back on in-store purchases, the same as using it in any other retailer.

Ironically, I only use the Walmart branded card at Smith's supermarket since it's a Mastercard and my other cards are Visas.  Walmart purchases get a Visa card with a larger percentage rebate.

Edited September 28 by Lou Schneider

A couple of weeks ago we stopped in Smiths in Henderson, NV. Had no gas points but they were running a promotion that when scanning your loyalty card it automatically gave you 3 cents off per gallon like Fast Freddy Myer. No such promotion here in Yuma at Frys. But I'm assuming it is in all of Arizona, Frys gives gas points on beer, wine liquor purchases the same as your groceries here in Yuma.

  On 9/26/2019 at 8:44 PM, SWharton said:

Be aware that Smith's does not accept Visa Credit Cards any longer. I don't know if that implies that all Kroger Supermarkets do not accept Visa CC. Smith does accept Visa Debit, just not CC. I had to leave my shopping cart behind as I did not have any other card with me at the time. The cashier did not know why.

I ran into this at Smith's in Taos, New Mexico, a couple of months ago.  There was a sign at the entrance about it, even though the policy had started back in April.

Kroger first did this a year ago, at Foods Co stores, which are all in California.  At the time, people worried that it was a harbinger for other Kroger stores, but so far, it's been only Smith's.

  On 9/30/2019 at 8:16 AM, Blues said:

I ran into this at Smith's in Taos, New Mexico, a couple of months ago.  There was a sign at the entrance about it, even though the policy had started back in April.

Kroger first did this a year ago, at Foods Co stores, which are all in California.  At the time, people worried that it was a harbinger for other Kroger stores, but so far, it's been only Smith's.

Which really is kind of weird, as if this is a trial balloon to see whether they so do this system wide or not.  Personally, because they don't accept Apple Pay (Android Pay) they won't be getting my business anymore.  

  On 9/30/2019 at 8:16 AM, Blues said:

Kroger first did this a year ago, at Foods Co stores, which are all in California.  At the time, people worried that it was a harbinger for other Kroger stores, but so far, it's been only Smith's.

Only at Smith's, or at Smith's and at Foods Co?

They aren't doing this randomly, VISA apparently has increased the fee that retailers pay to use the VISA CC. Above what Mastercard charges. So the stores are just refusing to pay it and if enough stores do the same Visa will have to back down.

I say good for them. It is the essence of capitalism to refuse to buy something when the price is too high.

Yes it is.   Just as it is up to consumers to decide what services they require  to part with our money.

  On 9/26/2019 at 11:52 PM, Twotoes said:

What ever happened to paying with cash?

It became obsolete and foolish, as well as a huge waste of time.  Right now the Amex Blue Cash Everyday card is paying us back 6% on groceries (yes, six percent, not a typo), and 3% on gas/diesel.  It would be crazy to use cash.  And it takes longer to get it, and use it, and deal with change.

Back on topic, Fry's here in Phoenix doesn't show any indication of not taking any cards.  Some stores used to be anti-Amex, and that's been my primary card for a while, so I'd just go to other stores.  Vote with your dollars.  There are lots of options.