This shows them that writing has a purpose and involves them in serious, grown-up business. Don’t worry too much about spellings and neatness, the idea is to promote writing as something practical that they can do, not something where they make mistakes or get things wrong.
Have them add picture clues if they like, especially if they’re shopping with younger siblings who might like to join in too.
And then when you’re shopping, let them be in charge – giving them the added practise at reading their list. Letting them direct the purchases might even make for a happier trip to the supermarket with less pestering now they’re in charge.