Most of which, yes, seem rather far-fetched. The one about focusing too much on the Greeks and not enough on contributions to mathematics from other cultures is a fair point. Sadly, without the rest of her article (if anyone does have it, a link would be nice), it's kind of hard to tell what she's saying exactly.
But whether or not the full article is as silly as it seems from the quotes, the way the same handful of quotes from the same single source are rapidly spreading all over the internet as supposed proof of academics gone mad should be rather concerning. It would be something else if this was some high-profile work by a well-known writer, but as far as I'm aware Ms Gutierrez doesn't have any prior claims to fame, and this controversy is really just being stirred up about one article in one not particularly noteworthy academic publication containing dozens of articles. Correct me if I'm wrong.
If you go looking for something to be offended about, no doubt you'll always find it. But if you then choose to take this manufactured outrage as representative of whichever class you want to condemn, it really says a lot more about you and your intentions than about the class in question.