I gather that bodyweight training is superior to weight training for gymnastics (http://www.eatmoveimprove.com/2010/03/the-fundamentals-of-bodyweight-strength-training/). However, I enjoy weight training more at the moment. Is there any danger that following something like this (http://stronglifts.com/5x5/) would actually be destructive to my long-term goals of gymnastics/parkour, or would it merely be nonoptimal?
Speaking specifically from a training for Parkour angle weight training (up to a point) would not be destructive to your goals.
Many advanced coaches and traceurs with exceptional jumping power recommend using squats to improve both impact absorption on landing and power output. With that said, if you're serious about Parkour or gymnastics you can lift weights, but treat lifting as supplemental conditioning. Working towards a 1.5x to 2x bodyweight back squat is definitely useful in the context of landing and jumping, which makes it valuable for Parkour. With that said, the SAID (specific adaptation to imposed demand, pun not intended) principle rules here, so spend most of your time improving the specific movement skills.
Weight training is awesome. So is body weight training. If you're lifting below 300 lbs in a weight program such as Strong Lifts, it shouldn't interfere with your bodyweight training.
However, once you start lifting really heavy weights, you might begin to see a decrease in your mobility and flexibility, which might hamper your bodyweight training. This is because the core principle of programs such as Strong Lifts is that your muscles need to get big in order to lift big. Bodyweight exercises depend on how strong your limbs (as well as your heart and lungs) can support your body. The bigger your body gets, the more you'll have to exercise in order to be strong enough.
If you search around the Internet for pictures of guys lifting heavy (400+), most of them do not have the strength to lift themselves in bodyweight exercises.
I'll conduct more searches on the topic and see if I can find articles to back up this theory.
I think doing some weights a couple of times a week would be fine.
My concern would be if you are lifting heavy weights every day and you bulk up too much.
For gymnastics/Parkour you need to be strong, agile and flexible.
Being too big will reduce your flexibility(range of movement) which could affect your agility. Having said that done in moderation, it will help with strength.
You also need to take care, as at 17 you are still growing.
So in answer to your question, mix it up. Some body weight exercises, some weights. Do what you enjoy, but keep an eye on why you are doing it, and keep it in moderation. Hope that helps