Is it legal to wear a string bikini shopping?

Whether or not it is legal to wear a string bikini while shopping depends on where you are shopping.

It would be improper to wear bathing suits to shop in most places. I am assuming you're not shopping on a beach market where it would be the norm. Be careful of immodesty laws as the beach is usually lax on enforcement whereas some markets would be very strict.

In an Islamic country just going outside let alone making it to a store to shop in a string bikini would most likely cause you to be arrested and beaten or at worst killed.