It is generally accepted that there is no experimental evidence that could determine between macroscopic decoherence and the collapse postulate.

From the Stanford Encyclopedia of Philosophy,

It has frequently been claimed, e.g. by De Witt 1970, that the MWI is in principle indistinguishable from the ideal collapse theory. This is not so. The collapse leads to effects that do not exist if the MWI is the correct theory. To observe the collapse we would need a super technology which allows for the “undoing” of a quantum experiment, including a reversal of the detection process by macroscopic devices. See Lockwood 1989 (p. 223), Vaidman 1998 (p. 257), and other proposals in Deutsch 1986. These proposals are all for gedanken experiments that cannot be performed with current or any foreseeable future technology. Indeed, in these experiments an interference of different worlds has to be observed. Worlds are different when at least one macroscopic object is in macroscopically distinguishable states. Thus, what is needed is an interference experiment with a macroscopic body. Today there are interference experiments with larger and larger objects (e.g., fullerene molecules C70, see Brezger et al. 2002 ), but these objects are still not large enough to be considered “macroscopic”. Such experiments can only refine the constraints on the boundary where the collapse might take place. A decisive experiment should involve the interference of states which differ in a macroscopic number of degrees of freedom: an impossible task for today's technology. It can be argued, however, that the burden of an experimental proof lies with the opponents of the MWI, because it is they who claim that there is a new physics beyond the well tested Schrödinger equation.

No mention of the anthropic principle? Lots of existing thinking in these lines under that term.

This seems to be a misapplication of Bayesian reasoning. Suppose I believe this argument, and as such, assign 99.9% to "no god, many worlds". Then suppose I had some absolutely reliable knowledge that god didn't exist. This argument stops working and I now believe "no god, collapse postulate" at 50% and "no god, many worlds" at 50%. Imagine that I am about to get that perfectly reliable knowledge about the existence of god. I am almost sure that I will get "no god". I know that, given "no god", I will assign 50% credence to collapse postulates. I currently assign <0.1% to collapse postulates. Something has gone wrong.

The Bayesian irrelevance theorem states that

The likelihood ratio of any two hypothesis depends only on those hypothesis ability to predict the data, and the likelihood ratio in the prior.

In other words, if you have 3 possible theories, X, Y and Z, and you want to compare X and Y, then you don't need to know anything about Z. To compare X with Y, compare their priors and their ability to predict data as if Z didn't exist.

This will give you the ratio of the likelihood of X and Y.

So, to compare the two hypothesis, "no god, many worlds" and "no god, collapse postulate" you only need to think about these theories, what their priors are, and what updates you can make.

Depending on how you handle anthropic reasoning, you might or might not make an update towards many worlds.

You don't need MWI to bump up the chances of lfe forming somewhere, just a large enough universe. Anthropics tells you that you should expect to find yourself on the one planet with life, if there is just one planet with life, in the same way it tells you that you should expect to find yourself in the one branch containing life under MWI.