If you taboo "anthropics" and replace by "observation selection effects" then there are all sorts of practical consequences. See the start of Nick Bostrom's book for some examples.
The other big reason for caring is the "Doomsday argument" and the fact that all attempts to refute it have so far failed. Almost everyone who's heard of the argument thinks there's something trivially wrong with it, but all the obvious objections can be dealt with e.g. look later in Bostrom's book. Further, alternative approaches to anthropics (such as the "self indication assumption"), or attempts to completely bypass anthropics (such as "full non-indexical conditioning"), have been developed to avoid the Doomsday conclusion. But very surprisingly, they end up reproducing it. See Katja Grace's theisis.
The other big reason for caring is the "Doomsday argument" and the fact that all attempts to refute it have so far failed.
Jaan Tallinn's attempt: Why Now? A Quest in Metaphysics. The "Doomsday argument" is far from certain.
Given the (observed) information that you are a 21st century human, the argument predicts that there will be a limited number of those. Well, that hardly seems news - our descendants will evolve into something different soon enough. That's not much of a "Doomsday".
r/Fitness does a weekly "Moronic Monday", a judgment-free thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. I thought this seemed like a useful thing to have here - after all, the concepts discussed on LessWrong are probably at least a little harder to grasp than those of weightlifting. Plus, I have a few stupid questions of my own, so it doesn't seem unreasonable that other people might as well.