"Naturalist" can be a good term when you have to have one, for the reasons you describe -- if it applies to you!
Of course sometimes you don't even want to make the label about your beliefs, because that plays into the religious notion that you have to have the right beliefs. Then "Secular" can perhaps suffice. 🤷♂️
In my circles a bunch of folk support either a pure-wave interpretation of quantum physics, a broader Tegmark-style mathematical universe, etc up to full modal realism.
Given an ontology like that, it's easy to show that certain kinds of theories are true in a superset of the worlds where more specific versions of those theories are true. Example: a child psychology theory with five stages of development versus a theory with those same five stages plus one.
It's a short poem but god I love its lines and I wish I could find a way to use them in conversation! e.g.:
> I love the way you wear your
> face, how you ride this life.
...
> Forgive my word-churn, my
> drift, the ways this text message
> has gotten all frothy.
Text: https://www.poetryfoundation.org/poetrymagazine/poems/56098/sea-foam-palace
Thrash no more 'gainst the storm in your skull
though drops splash, pool and spill unheedful
they culture a crop of facts and lies.
Farm your mind. Grow where you memorize.
Cut neat, plumb canals new 'cross the plain.
Place outlets for fateful floods to drain.
Dig cisterns to outlast the dry spells.
Level the obstinate sundry hills.
Bury old quagmires in barren earth.
Dredge or dam old beds by plan and worth.
Thus make swift the thought-stream's coursing tao,
effortless to flow from "How?" to how.
a quiet nerd with a head full of ideals