That being said, unless you're creating a service specifically for picky designers/developers, it doesn't matter. 99.8% of the Internet has no idea what Bootstrap is.
(ps: the folks who first made Bootstrap worked at Twitter, but Twitter let them take the ownership of the product with them as they left.)
To be honest with you, I think the only valid argument in here would be design taste: "that project is using mostly the standard bootstrap design,they don't invest in x yet" and that would be a valid just in half. The truth is there is a lot of projects that, even with different code, they all look the same with little variantions. In the end, it doesn't matter the skeleton, what it matters, imho, it's the service they offer.
Of course Twitter uses Bootstrap—it was made by/for Twitter. However, Bootstrap's defaults are based on Twitter's brand guidelines. That's part of the problem: with Bootstrap 1 and 2 basically every website made with Bootstrap looked a lot like Twitter. Bootstrap 3 alleviates that by encouraging customization and shipping with a flat appearance, but sites made with Bootstrap are still very similar to each other—developers don't customize it, and don't try to change some of Bootstrap's easily recognizable idiosyncrasies.
It reminds me of 2004/2005 when every web app was more or less trying to copy the aesthetics of 37signals apps.
There are endless websites with terrible web designs that provide valuable, reliable services. And there are endless more websites with good-looking, hand-built designs that offer no service of value and, could have their (plain-text) password database cracked tomorrow and disappear off the net forever.
Even if you are going to judge an entire company by the web framework it chooses to use, Bootstrap could be a good sign, as they are at least tech-savvy enough to know what that is, as opposed to using the default Wordpress theme!
Unless you're a code auditor, where you have time to spend looking and analyzing the code, there's no reason to not trust anyone who didn't code the website from 0. Bootstrap as well other frameworks are just that: a conjunction of best practices and some other modules that proven to work well across several browsers and devices.
We can argue speediness and all the yada-yada, but in the end, pro developers repeat the same things even missing one bigs when do all from 0. Using frameworks is a way to avoid those mistakes and, to have a development line well documented. You still can extend, trim the framework as you want.
Think other professions never distrust anyone because he's using that library, that gem, that framework. In the end everyone has limited time to execute work, so if other programers enjoy those libraries why the frontend ones don't?
Anyway, I think Bootstrap default theme (or slightly modified, but recognizable) is alright for young products targeted to "normal" people who have no idea about Bootstrap. I think it matters more for developers and designers and products targeted for them should invest in creating custom theme.
The only thing I'd look for would be EV SSL. No "green bar", no credit card.
By the way, some non-financial websites use EV SSL, such as Twitter. I don't see why Amazon can't get a cert.
Who cares what tech stack a web app is written with. It's like saying you wont pay for services that use rails, prototype instead or jquery, or a color palette you don't like.