store membership cards on IPhoneX

You do add them yourself, and the facility is the Wallet App.

I'm not sure what the issue is. If the merchant for the Loyalty card supports Wallet App its just a click to add them. either from their website, an email or their App.

If they don't support the Wallet App then they cannot be added to Wallet.

You may be able to add them to a 3rd party App: https://apps.apple.com/us/app/stocard-loyalty-cards-wallet/id444578884

Loyalty cards go in the Wallet app. View your membership card on the store’s app or website using Safari on your phone. If the card is designed to be stored on the phone there will be an “Add to Wallet” button on it.

Here’s more information→Add, use, and share boarding passes, tickets, and other passes in Apple Wallet - Apple Support

The Wallet app is a place for certified items only; the idea is, if it’s in the Wallet app it is legitimate. There are too many opportunities for counterfeit credentials if you could add anything you wanted to the wallet.