That depends. Some luxury materials can be machine washed. Long-fiber cotton, in particular, is a durable textile that can stand up to being washed in the washing machine and even dried in the dryer. In fact, cotton usually only gets softer with washes.
On the flip side, other materials might not be so machine washable. You'll want to be extremely careful with delicate fabrics like silk and synthetic fabrics, some of which cannot handle being washed in a machine with an agitator – or even in a machine at all.
No matter what kind of sheets you buy, the best way to ensure you're caring for them appropriately is to check their care tag and follow the instructions on the sheets. The care tag usually comes on the bottom corner of the flat sheet. Make sure to read the instructions thoroughly, and don't disregard any part of them. Doing so could mean ruining your sheets.