The rust on the grill of a barbecue or smoker poses only the slightest of risks, if any. You are unlikely to sustain a deep puncture wound with its attendant risk of tetanus, as you could from a projecting item, such as a rusty nail. And iron oxide from the rust that transfers to grilled food is harmless in small quantities.
Rust on the structural parts of any grill, charcoal or propane, or the burner ports of a propane grill can be more cause for concern. Learn to judge whether that inevitable rust that seems to appear overnight, even on carefully stored grills, could be a problem.
Clean rusted metal grates with a nylon brush, metal coil cleaner or grill stone -- and avoid the often-recommended and ubiquitous wire grate-cleaning brushes. Small pieces of brush can get into grilled burgers and other items and cause a trip to the emergency room. If you have to use a wire brush, wipe off the grate with a wet paper towel before cooking on it.