Those sound like nothing but excuses for being a terrible web developer.
"First is cost. Even if it only takes 10 grand to make a site "functional" in x browser, rebuilding an application to fully work with ie7 does not. If it takes 15-20% (or greater) more development time to add in support for IE7, but IE7 does not provide 15-20% increased revenues (it won't, unless you're making business software specifically for tech-agnostic corporations). You might say oh, it doesn't take 15-20% more time... just use jQuery and magic will happen. No man. It takes much more time."
Oh man, there is so much that is wrong with this comment.
First of all, users are more willing to buy from a service that works compared to one that, well, doesn't. That's just common sense. Secondly, if you really think that sprinkling some jQuery over a site will just make it work then I really hope that you aren't a web developer, because that mentality is exactly what is wrong with many websites out there today.
"Second is more philosophical. Assuming you are a consumer focused company like AirBnB, you customers are fully capable of upgrading to a new browser. There are no IT limitations on a personal computer. It takes all of 5 minutes and is completely painless. Stop coddling IE7 users; it is obsolete."
Again, if you are incapable of supporting older browsers it's probably because you're a terrible developer. Regardless, there is no philosophical debate here. Users can use whatever the hell they want and it is not your business to tell that what to use. It's entirely up to the client, and if there are users that are using IE6-7 it's probably because they are on old hardware or a machine that isn't theirs (i.e. a work or library machine). The limitation on a personal computer is just that. If your site takes ages to load are you going to suggest to the user to get a better internet connection or to buy a new computer?
"As far as pages working without JS: this is 2012, not 2002. If you still treat today like you treated 10 years ago, you really have no business complaining about anything on the internet. The internet is not for you, and neither is a site like AirBnB. If you think I'm being overly harsh, see my last paragraph. Installing FF, Chrome, or IE8/9 takes all of 4 clicks."
So, where do users limited to screen readers fall into your "the Internet is not for you" speech?
The reason many of us develop solutions that work across legacy browsers and screen readers is because we have the experience to be conscious of those who CAN'T view the web as you'd like to.
Again, it is not your place to dictate what users should be using. Regardless of their lack of browser support it is a wasteful site that is entirely dependent on JS and as such it is completely inaccessible.
It's comments like yours that give me "the fear" when talking about web development.