The problem of cosmological fine-tuning is never straightforward. It is not clear, in the first place, when it is legitimate to complain that a physical theory treats some phenomenon as a highly contingent ‘product of chance’. Where the complaint is legitimate, the cosmologist has several different means of recourse. The inflationary Big Bang illustrates how a change in dynamics can convert delicate dependence on initial conditions to a robust independence from the initial state. The bubble universe scenario demonstrates how low individual probabilities can be overcome by multiplying the number of chances. And homeostasis provides a mechanism for variable quantities to naturally evolve to special unchanging values that could easily be mistaken for constants of nature.Me: I think he's right--it's not straightforward. Back in 1999 I first delved into this topic, in a cover story for Reason magazine (I link to a PDF since the article as currently posted on Reason's website has an editorial glitch) and my focus was on rebutting claims from journalists and conservatives that science had "found God" via supposed fine-tuning in physics. I returned to the subject in subsequent years including here and here. While I continued (and continue) to think the religion-from-physics case is weak, I also came to see some skeptics seeking to bat away the religious pitch as themselves being a bit too cocksure, about multiple universes and other cosmic speculations that bolstered their atheism. My 1999 article, I think, did a decent job of suggesting how little we know, cosmically.
My original piece, though, is a bit dated in that some of the physics has been added to or superseded. Maudlin has a good discussion about Alan Guth's inflationary model (which I'd cited) and the uncertainties that have developed about what it does or does not indicate about fine-tuning.
Finally, take a look at the chart below. It doesn't show a physics phenomenon but actually is what I got from Google's Ngram viewer (which tracks book mentions) when I plugged in "anthropic principle" for the years 1970 to 2008 (the most recent data). As you'll see, mentions of that phrase declined in the first decade of the 21st century. I suspect that's because the debate over whether physics had "found God" cooled down and the term lost some of its hot-button appeal. If so, I like to think I helped push the discussion into a less polemical and overwrought place. (If you have trouble viewing the chart, mea culpa and click here.)