Red Bull, among other energy drinks, sometimes get a bad rap. Like most things, too much of something is not always good and in the case of highly caffeinated foods and beverages like energy drinks, drinking too much can pose potential health problems. How much caffeine your body can handle may be very different from another person's and you might feel nothing at all while someone has had way too much. In a typical 12 ounce can of Red Bull, there's 111 mg of caffeine. That's actually only a bit higher than the average 8 ounce cup of coffee, which has about 90 mg of caffeine. In fact, when compared among other caffeinated energy drinks, Red Bull has about the least amount of caffeine.
Like anything that has caffeine, drinking too much can lead to heart complications (like an irregular heartbeat) and neurological issues. Among runners, energy drinks aren't really shunned so much for their caffeine amounts (because you can experience health complications from too much caffeine no matter HOW you consume it) as they are for the mixture of high caffeine and high sugar. Runners tend to be pretty health conscious people, and most try to practice food moderation to help improve their running performance. Therefore, many are overly aware of sugar amounts in foods, and like to avoid consuming too much. This is probably the real reason why you've heard people advocating against energy drinks like Red Bull. Another reason could be that caffeine sometimes dehydrates body. A lot of runners are avid coffee drinkers, but they also make sure to fill up on plenty of H20 along with their coffee, as well as throughout the day.
As long as you consume Red Bull in moderation and make sure you're still getting enough water, you will likely be fine. The caffeine and sugar might actually help stimulate your running performance for the better, as long as you limit yourself to a can or so a day. If you know you have a sensitivity to caffeine, always check with your doctor before you start drinking energy drinks!