I don't agree with many of the things written in the this post.
Unlike what this article implies, it is not just Christian apologists who argue for the fine tuning of the universe. A brief introduction, publish in a peer-review scientific journal, is here (and feel free to check out the also peer reviewed references):
https://arxiv.org/abs/1112.4647
The article claims, several times, that scientific papers like this are considering too many parameters and should only consider those in the (much simplified) LCDM model of cosmology.
They are not even considered variables in the modern standard cosmological model.
But if you're considering the properties required for life you do need to consider parameters other than a large scale model. The cosmological model only captures basic features of large-scale cosmology, such as the average density of the universe. It does not capture parameters important to chemistry and biology, such as those to do with the standard model (of particle physics). If, for example, no stable matter could exist, it seems very unlikely that life could exist. So, yes, you need to consider more than just the lambda-CDM model, as that (intentionally) is a vastly simplified model only meant to capture large scale effects.
He singles out carbon, and implies it doesn't need fine-tuning. But in his own link, the Professor who carried out the study says the exact opposite:
Professor Ulf-G Meißner, in explaining his new groundbreaking study, states: “The Universe we live in is characterized by certain parameters that take specific values that appear to be remarkably fine-tuned to make life, including on Earth, possible. “
“For example, the age of the Universe must be large enough to allow for the formation of galaxies, stars and planets, and for second- and third-generation stars that incorporated the carbon and oxygen propagated by earlier exploding stars,” he says.
“On more microscopic scales, he adds, “certain fundamental parameters of the Standard Model of light quark masses or the electromagnetic fine structure constant must take values that allow for the formation of neutrons, protons and atomic nuclei.”
And specifically on Carbon, he's says his study shows this fine tuning:
“From the observed element abundances and the fact that the free neutron decays in about 882 seconds and the surviving neutrons are mostly captured in 4He, one finds a stringent bound on the light quark mass variations … under the reasonable assumption that the masses of all quarks and leptons appearing in neutron β-decay scale with the Higgs vacuum expectation value.”
"Thus,” Professor Meißner states, “the Big Bang Nucleosynthesis sets indeed very tight limits on the variations of the light quark mass.”... “Such extreme fine-tuning supports the anthropic view of our Universe"
The post claims that people who disagree with it, don't understand probabilty. But then goes on to say that an atheist assigned the existence of God a probability of 10^17. If you're going to use ad hominem as an argument, at least make sure your probabilities lie between 0% and 100%.
Regarding a multiverse, the author posits that an infinite multiverse (presumably each with different parameters) might exist. Perhaps, but that commits the person to the logical consequences of that - that exact copies of us exist, that the easter bunny and Santa Claus exist, and that every Greek and Roman god exists. The claim that any (or worse, all) of these things exist seems, prima facie, to have a very low probability. How this article can suggest that it is 10^17 times more likely than a monotheistic God existing needs more work.