This was a concern for me the first time we took our stroller but now it doesn't cross my mind much. I got a used Mac Twin specifically for Disney trips (we only go every 2-3 years but seriously the stroller gets used for nothing else LOL), but from what I read, the issue with strollers like that is that people more often end up grabbing the wrong one since there are so many alike. So I just tried to mark ours well. We put some contrasting colored tape on the handles and zip-tied a laminated card with our last name and cell number on it on the bottom of the basket so that if it got mixed up OR we left it somewhere, we might have better luck tracking it down. We don't leave valuable things in the stroller though, as THOSE types of things have a better chance of getting picked up (we have left a blanket or something in the basket for some rides, and sometimes if we have some small souvenir bags we will leave them underneath of it, and while nothing has ever been stolen, those are the things I know would be all my own fault if they did).
I am more concerned with my stroller getting broken or something by the airlines than stolen.