I see this kind of thing in every gear recommendation thread where someone uses the word punk. I mean this respectfully, but frankly: I'm going to have to say that you'd sound like a clueless outsider to anyone involved in an actual punk scene.
Punk means a lot of things to a lot of people. Yes, The Sex Pistols and The Ramones play "punk rock". I'm not going to dispute that as a name for the style, because that's what most people call that style, and that's how language works. When most people use a word to mean something, that's what it means. But those bands were hollow from the very beginning. While DIY punk scenes sprung up and thrived all over the world, those guys dressed like punks and talked like punks, and there were very very influential in punk culture, but it was all an act. When they signed their major label deals, they ceased to be participants in the culture itself. They were still icons, but not participants. Bands like Crass and Minor Threat were able to be just as influential AND maintain their integrity. The scenes these guys were a part of never died.
It's important to separate punk culture from punk rock as a style. In the DIY scene, you'll find every kind of music claiming to be punk. No ones puts other bands down for not being punk because they don't sound like classic punk rock. Folk, metal, electronica. That can all be punk as far as the punks are concerned. But you can also play punk rock and not be a punk band. Like The Sex Pistols. We all love Sex Pistols for their music, but no one respects them. Sid Vicious couldn't even play bass. Johnny Rotten just puts on this absurdly fake attitude. It's all pretty dishonest. But you get these outsiders to the scene saying "punk is dead" or "punk is all about attitude", meanwhile there are scenes that have been active since the 70's and new ones popping up in smaller cities, and bands putting out seven inches and silk screening their own t-shirts to sell in dirty punk house basements and not even trying to get big because they're not in it for the money. And the music has evolved so much. 80's hardcore turned into metalcore, emo, screamo, hare-krishna stuff, crustcore, twinkly indie, and ton of other sub-genres and -cores I can't remember. A lot of those subgenres have turned out bands that got big and put out great records, or got big and put out uninspired crap, or didn't get big but still got stale, or didn't get big and stayed fresh and interesting. All that makes you punk is being part of the culture, regardless of how you dress or what kind of music you play or how much attitude and aggression you put on.
Now, not letting stuff stop you is a big part of punk culture. Whether your attitude is "3 chords, start a band" or "my Squier Strat won't stay in tune but whatever I'll keep playing" or "I'm not into guitar so I'll start a zine", lack of knowledge and lack of gear isn't something that's going to hold back punk. But that doesn't mean that caring isn't punk. And I mean caring in more than one way. A lot of bands grow, both in terms of skill and gear. They care. If you're not going to do better when you can do better just because it's not punk, then your punkness is really just an empty affectation. On the other hand, there are definite trends towards certain gear within punk culture. Punks care what their heroes play. Gibsons are pretty common, in big part because of The Sex Pistols, but also because they were a brand name that was relatively cheaper in the 80's when superstrats were in. And punks tended to be pretty disgusted with hair metal and new wave. So all the 80's bands were playing Les Pauls that were made in the 70's. There were a lot of 70's SG's in the 90's/early 00's screamo scene too. Most of those were probably stock, T-Tops or whatever else Gibson put in there at the time, but more than a few punk guitarists upgraded to Super Distortions. So when you say that punk is routing a Dano with a screwdriver, you're missing the point that the culture favours certain gear, which is what people who make threads like this are looking for information about.
We can go on all day about punk being about whatever, but CUCA has given us a pretty good list of the bands that HE wants to sound like, so there's no ambiguity there. According to Duncan's artist list, the guy from Bad Religion uses a Custom Custom and a Distortion. The guy from NOFX uses a Custom. All the other bands I had to do an image search for, and every single one has a pic with their guitarist playing a Les Paul, so the 498T is probably still in many of those. I see JB's used more by guys playing through high gain heads looking for more metal tones, not the other way around. I did notice a few years back that Telecasters were becoming more and more common, and they all seemed to have JB's in them and run them into Oranges. I'm not sure if those guys are still doing that though. The players who have more traditional influences tend to favour the Custom or Custom 5 these days, if they swap their pickups at all.
The only band in the realm of punk that I've seen using an Invader is Blink, and even then a lot of their albums were recorded with a stock Les Paul. Tom Delonge plays a hollowbody with a Dirty Fingers a lot these days too. I bet you could do most kinds of punk well with an Invader, but I just never see punk bands using them.
Some day I would like to play through a delicious hambucker.