Well.
My thesis (12 years ago, before I learned that coding paid a lot better than philosophy) was a survey of how the argument from design had developed post-Darwin, and part of that involved digging into arguments being made by physicists who had no particular religious affiliation but still felt that the Goldilocks-ness of our universe was something that needed explaining.
And it turns out a lot of those people find anthropic arguments to be, at best, unsatisfying; at worst, they can point to logical fallacies underlying anthropic attempts to explain away the conditions of the universe we find ourselves in.
The interesting arguments, to me, fell into two camps:
1. Natural selection operating on the level of entire universes. Several different theories postulate singularities as a source of new universes, which in turn means that a universe in which conditions allow for significant gravitationally-bound accumulations of matter will have more "offspring" than a universe in which they don't. Thus, physical constants which are conducive to life are likely to be more common than otherwise expected, simply because (coincidentally) those conditions are the ones which give rise to significant gravitationally-bound accumulations of matter.
2. Arguments in favor of simulated universes. Paul Davies (if you want a name to look up) has a few layman-accessible articles arguing about the probability of this, and working from the fact you only need one life-supporting universe -- which is likely given various of the multi-universe theories -- to kickstart the process and wind up with a far larger number of life-supporting simulated ones.
There are also people who make arguments in favor of a more traditional religious conception of "God", but do so from the standpoint of regularities in physical law. Those are less interesting to me personally for a few reasons, but they are out there.