I don't think it's considered a conflict of interest unless you are in the same department within each company, and even then it might only matter with certain departments. Obviously you can't do Market Research with Universal and Disney, but I'm sure you can be in Entertainment for both and it be a non-issue. I know a ridiculous amount of people who work for both companies and it's not an issue.
The best reason someone wouldn't hire someone is lack of experience and not exuding confidence. Theme parks are a high capacity place where you need to be social and interactive. If you can't do that with the interviewer than it's going to hinder their ability to think you can do that within the resort. If you have a resume with experience bring it, it'll boost your chances.