Calling me Mrs. Fleming doesn’t mean I am old!
In a professional situation, it is not polite to call new acquaintances by his or her first name. You should wait until (or if) they ask you to call them by their first name.
In social gatherings, it may feel awkward to call new acquaintances by their last name especially if they are your age or younger and in this case, a casual gathering, using first names is fine. If someone is introduced to you by only their first name, then of course you call them by that name.
It is incorrect for children to call adults by their first names and it is also disrespectful. Although most people have a desire for comfort and casualness, it takes the same amount of energy to say “Mr. Whatever” as it does to say “Bruce”, yet the difference in common respect is immense.
Until someone has given you permission to use his or her first name, you should always go with the last name, a very dignified gesture that has nothing at all to do with implying that someone is old because they are being addressed by their last name. Adults should accept this respect for his or her personal space and realize that it also has nothing to do with perceived social superiority/inferiority. It is simply a matter of kindness and respect for personal distance.