In my country, given our size we have an incredibly high murder rate, and of course we got the whole theft and holding up people thing. I won't sugar coat it, because its true, but there are outlets out there that try to instill ridiculous and unnecessary fear in our tourists. Why do I say that? Because 90% of all murders are gang-related (rival gangs killing off each other basically), and the theft well, as we all know that is a random thing that happens EVERYWHERE, but thankfully almost never includes murder along with it.
Why do I bring up this anecdote? I have plenty of people who try to convince me that I need to be terrified of my own shadow. "Don't go out at night" "Don't carry your purse with you" "Make sure you keep a bat in the car", but you know what? I live life how I want. I am very cautious and I know which places to avoid at what time of day, because of the heightened likeliness of being targeted. But I can never bring myself to feel 100% unsafe the way other people do. I've learnt that the first step at keeping yourself safe is to be very observant of your surroundings. Be aware of the people around you. It really does help take some of my vulnerability away, and in return makes me worry less. And this is something I carry with me even when I travel. When travelling, I try to be very aware of what areas to avoid, or which ones are considered "safer" by locals, but keeping in mind that nothing in life is guaranteed, including safety.
We will be going to Disney in October, and by then most of this would probably be more or less closer to how they were before the tragedy happened. In the meantime, my sister will be going to two concerts in the US in July. I worry a little, but I don't see the point in keeping yourself locked up in your room because you worry about the "could bes". We could walk outside today and be run over by a bus for all we know, but that shouldn't keep us from walking outside.
I have every confidence that there are people out there who are trying their best to keep us safe at all times, that's why don't have issues with TSA, or lines at the parks or anything. Its a welcomed inconvenience. Don't worry, the world is in alert right now (especially Florida), so there is a very slim chance anything could happen. Just have fun and live in the moment!