Is it permissible to purchase products online using stolen Mastercard and Visa cards from the West?

It is not permissible to steal cards. Whoever takes money with them must return it to its owners if they are able. Otherwise, they should give it as charity to the poor or spend it on general Muslim public interests. The fact that the cards belong to Westerners does not make it permissible to steal them, as their owners could be Muslims. Even if they are disbelievers, the wealth of those with whom there is a treaty, those granted safe passage, and dhimmis is inviolable. It is also not permissible to interfere with the wealth of a belligerent if a Muslim enters their territory under safe conduct.