Should my tests fail when a variable value changes

You have automated tests / manual system tests.

Should they fail, if a variable value changes so for example:

You have an e-commerce website that has 10 products. In production, the price change is made and the testers know what the new prices are.

But you don't update the prices in non-production environments, but the testers are saying that their tests are failing as they have updated the prices in their tests. Because they have updated the prices in their tests.

My question comes down to, how the tests are written. Should they know the price of the items, or should they just know the business rules and test these.

If a price is needed to be shown on a screen, the tests should be written in a way that identifies this and the actual value shouldn't matter just a case of knowing where the data comes from and where it should be shown.

Thus in my opinion tests should only need to change if the business rules / requirements change and not that the data has changed value.