First, I want to say that I think we can all understand the reaction. We can all get our fur up when our child is in danger and it is not always logical.
Second, I want to say my reply is about the OP but also the general situation...
There are often a lot of posts about moms of toddlers who get frustrated/angry with the "big kids" (usually about 5-7 yrs old) at the playground, museum, pool or other places with a theme of "mean" or "not sharing". To mothers of toddlers, these kids seem so big and so "kid like" and in control of themselves and their toddlers seems so small and vulnerable. It true- there *is* a lot of growing in that time. But what often does not get addressed is that 5 year olds are not really that *big*. They have not mastered the empathy thing or fully understand why you can't play tackle or rough house with a toddler like another child. They do not understand that *your* child doesn't understand taking turns and will often retaliate when they feel they have had something unjustly taken from them. They don't get that a 6 foot fall is a big deal to push someone off of, or if you pull something out from under someone they will fall. They don't understand that manipulating them in play ("YOU, toddler, go get the shovels and I'll dig!") is unethical. They don't have perfect impulse control and may still hit or kick or push or throw things on occasion. And the flip side is that mothers with toddlers have not yet had the experience that someday, their own 5 year old will most likely do something "not so nice" either. When their children are 5, they will understand that 5 is still very, very young. But they are not there yet and only see the toddler now. But I can say 5 year olds doing these things- It is part of the process, and it is part of this time of life. Most 5 year olds can act very "kid like" most of the time and from the outside it can seem like they have more self control. But there are still "bits of toddlerhood" in there and they have their moments. Do we have to like it? Of course not. But I do think we do have a responsibility to understand it if we share public kid spaces with them.
So, while I understand your reaction, try to put yourself as the mother of the 5 year old... (Yes, she "should have been there" and all that, but imagine your child, at age 5, did this while you were digging in your purse for your ringing cell phone or something). From your description, what you did was more than just a firm tone (or even "yell") to back off or stop. You said you "lost it on him" to the point where a bystander told you that your behavior was inappropriate. Knowing that your young child as a 5 year old would be a good person who was still learning the ropes about how we treat people, what if someone said those things to *your* child when they made a bad decision? What if your beautiful 5 year old had a lapse in judgement (as 5 year olds do and is totally developmentally appropriate) and a stranger "lost it" on him yelling to the point that made adults uncomfortable and other children cry?
I think it is totally OK to stop a child from hurting yours. I think even a firm tone is reasonable. But I think taking charge of your own child and moving him or leaving is your first responsibility and the next is to find the other child's mother and talk with her if it calls for more than that.
I believe the "Golden Rule" applies to dealing with other people's children- Do unto them as you would hope strangers would treat your child if the situation was reversed.
So, while I understand that we first empathize with our own child and that our protective reflex can sometimes cloud our judgement, I think you will need to think about how you will deal with this in the future. I can give you a 100% promise that your child will be pushed, kicked, teased, denied a turn, whatever in the course of childhood (and most will just be the scrapes of life and forgotten 10 minutes later without a big deal, but they will happen). And, I can pretty much guarentee that someday, your child will be on the other end *doing* it as well (and will most likely be an innocent passing lapse of judgement or lack of understanding as they learn, but again, it will happen). This is a great opportunity to think about what lessons you want to teach your son about the words and options he has when he is in a bad spot with others, and about how you can deal with this in the future.
The mama bear can be a strong, powerful force that in some cases, keeps our babies alive and we women and mothers can and should be proud of ourselves for our fierce protection of our children. Truly, the mama bear urges are a gift we have of a force greater than ourselves at times. I know for myself, if my child were in serious and/or intentional danger, only G-d would be able to stop me. But it must be harnessed. The mama bear off-leash can be destructive. Counter-productive. Be proud of your mama bear. But make sure she is pointed in the right direction. A 5 year old does not need (or deserve) the mama bear. He might awaken her out of instict, but then you gotta put the clamp on her and look for other tools. Save the mama bear for when you really need her. Letting the mama bear out of her cage is a last resort, not a first line of defense.
And, for the record, I consider myself a GD mom and sometimes I yell. Like another person said, there is a difference between "loud" and "cruel". GD does not mean that we are always perfect pictures of zen parenting. It means that we can be ourselves (even in anger and frustration) without the cruelty and power and that we try to see these mistakes as chances to grow. I know in my case, that is not always a quiet or peaceful process! In our house, we are ethnic, loud, and deep in the trenches of living life. GD is not about giving up yourself or your own emotions or hiding how you feel. It is about communicating and responding in ways that understand that children are people too.
Also for the record, I currently have a 6 year old AND a 2 year old and sometimes, the mama bear can be in conflict with herself! My 6 year old did some minor "not nice" thing to the toddler, and I remember my mother scolding my 6 year old and my mama bear fur got twisted two ways! My toddler could be hurt! Don't talk to my 6 year old that way! Ha!