I would never muzzle Oscar unless there was a reason (his behavior). I just think they're plain cruel and you're being forced by society to do it to your dog because of THEIR ignorance. I take Oscar everywhere, yes I see the looks, yes I see people cross the street, yes I hear the whispers etc. Do I care...hell no. I also get ppl who come up and comment on how beautiful he is and well behaved. Sometimes the ignorances does upset me because I'm disappointed that society can be sooooooooo ignorant and if they actually took the 2 seconds to meet my dog, they'd see he's the biggest fur-baby around.

He's always well behaved out in public, he LOVES people and he listens very well off leash etc. My dh owned a rotti years ago and when we got Oscar as a pup he warned me all about this and people prejudices against the breed etc. I just let it roll off my back now, ignore the stares, ignore the people crossing the street and just focus on this big, wonderful ball of fur who brings me TONS of joy!
As for dog parks, I think they're a nightmare waiting to happen. It's not my dog I don't trust, it's the 500 ankle biters who've had zero training and who's owners have zero control over. An uncontrolled dog bites your dog and your GASP! Rottweiler defends himself....guess whose dog is getting put down????!! It won't the little yipper, it'll be the mean, vicious rottweiler. Don't feel that you're slighting your dog by not taking him to a dog park, you're doing him/her a favour. Oscar doesn't get to play with any other dogs actually because no one wants him to play with theirs. We just make sure he gets tons of attention, exercise etc. I highly doubt he's missing out on "dog play". That's not to say I wouldn't let him play with other large dogs, just under my terms and in a controlled environment (i.e. my backyard, not the dog park).
When I leave work on sunny days in a hurry, the guys always laugh and say "going to go clear the beach again?" LOL!! Because they've all heard my stories of taking Oscar to the beach off leash, looking around 2 minutes later and it's now empty! hahah! I could careless...seriously! We have a ball on the beach during low tide, if people are freaked out of my dog...sucks to be their dog who just missed out on a good time at the beach. Keep in mind my dog stays with me, always listens to his commands and has never, ever ventured off towards anyone/dog on that beach. He's not interested in anyone, anything but playing with us!
Get the muzzle off your dog, he hasn't done anything to warrant it. Learn to let peoples ignorance roll off your back and just focus on your dog.