My wife has an app that is basically a card holder. Instead of pulling out a loyalty card, she pulls up the one app that has all of them scanned/copied. It's great.
Nice. I used to have a handful, and now I just don't bother with the loyalty program at all. My local grocery's program is mediocre at best (discount at a gas station I don't use) and isn't even required to get discounts, so I don't bother. And they don't even need an app, just a phone number, so I just refuse to tell them my number because I'm getting zero value from it.
Likewise for pretty much everything. The only one I actually use is Target, and that's because I get 5% off using their debit card, plus some random discounts through the app. I don't go there very often, but when I do, I'll generally time it when there are some good discounts to stack (usually it's for birthdays or school, and I have a month or so leeway in when I go).
No, we avoid our local Kroger store (different name here), but when we go, I use my parents' number since they go there a lot and frequently use the fuel rewards. Our local grocery is supplied by Associated Food stores, which has the "Food Club" and related store brands.
The main options in my area (Utah) are:
Kroger sub-brand Smith's - not very convenient in my area, but the stores are large and have everything
Associated Food brands - smaller, more plentiful stores
Walmart/Sam's - I avoid like the plague, but they're just as plentiful as AF brands
Target - crap quality and high prices, not an option at all
Costco - good selection and great quality for the price
random specialty shops - higher price, but niche selection
Most of our spending goes to Costco, most of the rest goes to specialty shops, and we fill in the gaps with the local grocery chain. We spend something like $100/month at the grocery store, so it's not worth interacting with their loyalty program.