Look, I haven't been to a "public range" in many years. There are many reasons for that, and it's not limited to avoiding stupid gun handling. But I'll share my thoughts with you as they're related to your problem.
First, we need to define what's meant as a "public range", as people have different definitions of what constitutes public. I shoot on ranges operated as private, member-only facilities. Public ranges can be interpreted as pay-per-hour rentals, either operated as "open to the public" businesses or private facilities that charge premium rates for non-members. Or they can be public property, open to all taxpayers. Range Officers can be present or absent at any of those arrangements.
My general assumptions of those who use publicly-accessible ranges is limited to my own local region, but it's my approach and it guides how I deal with people who use them. I am fully aware some have no other options than to use these. If my assumptions and comments don't apply to anyone reading this specifically, then don't take offense at them.
In my own life I make very little effort to educate those choosing public ranges to shoot. We have over a dozen private membership ranges in my area. With only one exception, none of them charge even $100.00 in dues. They range between $20 and around $85 annually. In my area, I feel someone who will not pay a relatively small fee to have a well-maintained, well-controlled place to shoot also has little interest in putting forth the effort into learning competent gun handling skills. For him, it's a leisure activity.
A person who shoots as a leisure activity will not appreciate my attempts and efforts to educate him. So I don't try.
Those who are interested I work with, usually to find them places and ways to get those skills.
Those who are both disinterested, and do dangerous or stupid things with a gun I deal with differently. I do not attempt to educate those people. I simply express what I will not tolerate around me or those I care about. My responses depend on the situation. If no Range Officer is present, or the situation requires immediate attention, I'll handle it myself.
It's ranges from:
Sir, you'll need to be careful with where you point that while you're here. I've been yelled at before for being careless with where I pointed my muzzle.
to:
Uncle Rick, if you point the muzzle of that thing at me again, I'm going to shove gun up your ***
I only try to educate those who are teachable. Everyone else gets told the way it's going to be, either politely or in the most direct terms. But I don't let things like age difference, or even family relationships get in the way. I've kicked people off of a range before. I've told people twice my age to put guns away, or go someplace else to handle them.
If you're looking for ways to educate people, develop your socials skills to first determine who is receptive. Then figure out ways to approach them. You will probably have zero influence over a stranger, unless they specifically ask you for help. You'll have some influence over the people in your life that you know. If for whatever reason you aren't the right person to teach them, take some time and research what resources you have in your immediate area that you can recommend they take advantage of.