is it safe for babies to ride in convertible cars and why?

As long as someone doesn't let them blow away ;)

If there is an airbag for the front seat it isn't safe (in fact it
will do a lot of harm). Car manufacturers assume that the front
passenger is over 5 feet tall (over age 11)

If there is no airbag then push the passenger seat as far back as
possible. For babies under 9 months old and 20lbs they should be
rear-facing. Once they are over 9 months old and 20lbs they can go
forward-facing. These are the current UK recommendations.

With many cars you can disable the airbag for the passenger. However,
be warned that it may invalidate your car insurance.

If there are seats in the back then statistics suggest that the seat
behind the driver is the safest in the event of an accident.

Riding with the roof down is likely to result in an unhappy baby due
to discomfort. Most babies do not like the wind.