It is safer but not completely safe-
New airbag designs are safer than old ones. They reduce the risk to kids and other occupants, but they don't eliminate it. The main risk to kids in front is the frontal airbag, though the dash and proximity to the front of the vehicle add to the risk for all passengers in front. Side airbags are usually less of a concern. Some vehicles use sensors that disable them if they detect a child or small adult in the seat. Even so, sensors can be tricked, so they are not foolproof.
The recommendation is to keep kids 12 and under in back, regardless of their weight. Most vehicle owner's manuals will also state this. This is also the policy of the NHTSA, American Academy of Pediatrics and all other child passenger safety organizations.
That may not help you convince them. Sometimes people cannot be convinced no matter what you use to persuade them. They simply don't believe it can happen to them. That is part of the reason motor vehicle crashes are the #1 cause of death for kids and adults, ages 1-34 :-(