It is okay for you to refrigerate strawberries, though you can also keep them at room temperature for a while.
Those who purchase strawberries from the grocery store should get them into the refrigerator as soon as possible though, because it will slow down the decomposition process significantly.
If you want to keep your strawberries around for a while, you will definitely want to consider putting them in the fridge when you get home. By doing this you will be able to keep them from going bad for quite a while. The average lifespan of strawberries in a refrigerator is anywhere from two to three days at most.