Don't worry about getting off to a bad start, this is an interesting topic and it's better than just arguing over whether Travis "sux" or something of the sort - so let's get to it!
My normal attire is pretty scruffy. I hate clothes shopping, so I make do with stuff basically until it falls apart and I'm in danger of getting arrested for indecent exposure. But if I get a call to play at a primarily classical performance - which has happened before... well... I wear a decent suit. Ditto a jazz gig. If I get asked to play a metal gig then out come the old scratty Tool T-shirts etc. It's just the same for working. If I'm going into work at a fairly informal media company then I'll just wear pretty standard stuff (avoiding the scratty Tool T-shirts, of course), yet if I'm getting called to go somewhere where they have a dress code then I dress up. The reason for this is basically that dressing deliberately different from the people around you is a very loud shout for attention and generally speaking I'd rather demand attention through my work before my appearance. It's better to understate your appearance and overemphasise the quality of your work, generally, otherwise people tend to think you're a bit of a ("indecent piece of anatomy" - Ed).
You see my point? How I normally dress isn't an issue, because any out-of-place dress on a gig (be it a suit on a metal gig or a metal T-shirt on a jazz gig) immediately calls attention to the person wearing it. Ditto behavior. Now, that's cool if your role is to call attention to yourself - but that's a cross-applicable thing which also reflects on your playing. So if you're dressed like a maniac and playing like a maniac I don't see an issue with that - see Terry Bozzio on the Zappa "Baby Snakes" video. He's SUPPOSED to be taking a lot of the attention because he's a focal point in the band both musically and visually.
But then you have something like Travis Barker here. Now, either they hired him for freakshow reasons and they don't care if he plays like he does in Blink 182 as long as they can attract the "yoof" demographic, or they DO care how he fits into the band and they want him to be appropriate. I'd suggest that the differentiation isn't made between playing and appearance here, because they both reflect on the same thing in the performance: Is this person a focal point in terms of attention or not? Travis on this video just looks to me like he's trying to make up for the fact that his playing isn't a focal point of the music by looking and acting like he's on a completely different gig. That don't impress me much, so to speak...