If you are considering storing your firewood rack inside of your home then this is a question that you definitely need to pay attention to. In regard to if it is safe, it certainly can be. Here is the deal; as well as you know, when you transport wood into your home there may be a few critters that come along with it. If you ensure that the wood is cleaned and processed before you store it inside on your rack, then you should be just fine.
Then again, there is something else you need to keep in mind. When outdoors, wood is exposed to constant airflow and this will not be present indoors. As such, it may not age as well as it would outside. Of course, there is also no chance of it being exposed to the elements, so it works both ways.