This phrase usually implies strong disapproval of the item or idea in question. I wouldn't give those rude comments houseroom, they're completely unacceptable.
Pro Tip 2/3
Metaphorical Use
Often used metaphorically to express rejection of concepts, not just physical items. He wouldn't give the idea of cheating houseroom in his thoughts.
Pro Tip 3/3
Personal Standards
Reflects personal standards or taste when refusing to accept something. She's so picky with decorations that she wouldn't give most knick-knacks houseroom.