1. Good typography does not draw attention to itself. Most people will only notice your typographical work when you get it wrong. When you get it right, the reader takes in the information and registers the mood without ever noticing the medium.
2. There are snobs, who will artificially exaggerate the differences between fonts to try to appear more knowledgeable. There are differences between fonts and they really can create very different results. However, sometimes there are two well-designed fonts that happen to be very similar, and you really could use either with good, professional-looking results. Arguing about which of these fonts is "better" invariably generates more heat than light.
In other words, if you're not a trained designer, you're supposed to be font-blind. And if you are a trained designer, your reader should be font-blind. If they are noticing the details of which font you use, you're probably not doing a very good job.
The key, and this is important, fonts have historical baggage and they also are designed by relatively few people. After doing this, you start to see designer-traits and also historical influences. The hardest thing to see is white-space, which is another "i know kung fu" moment.