This question that relates to foundationalism: that all systems of thought must begin by making basic assumptions that are in turn used to get any system of knowledge 'off the ground'. Some putative examples (I don't necessarily agree on any of these being unsupported) might be: assuming the reliability of the senses allows me to make inferences from sensory knowledge, the assumption of the utility of reason to accurately know the world allows me to rely on reason, the need to assume that others experience a first person ontology, allows me to enter into meaningful discourse with others, etc.

(Note: One's epistemological starting point need not be foundationalism. One may employ other models instead, such as coherentism, (which denies that there is a need for foundationalism as there is no infinite regress problem), contextualism and pragmatism, which 'sidesteps the issue' by looking at the value of any human practice. Of course, one could also combine elements of any system, particularly if one is a Hegelian!)

Now, I'd like to talk about naturalistic assumptions.

There are two types in my estimation: axiomatic knowledge, which is defended by retortion, and basic assumptions that are not defended through retortion.

Axioms of reason would include the axiom of existence, identity and sentience. They are defended by retortion: any attempt to refute these axioms must rely on them in order to make the refutation, leading to a stolen concept fallacy: i.e. an internal contradiction.

So we can be certain that these axioms hold. Unfortunately, these axioms don't tell us anything about the 'world' around us, other than that 'something' exists, that whatever exists, exists as one thing and not another, and that these deductive truths demonstrate that we, the gleaner of these axioms, must be sentient, seeing as we are aware of these axioms. If all we wanted out of life was a very basic metaphysic grounded in bedrock certainty, we would be content. If we want more, we must move past these axioms, and risk error.

And this is where a naturalist foundationalist would move to basic assumptions: self evident 'first principles' - beliefs that any natural being seems forced to make in order to operate in the world.

(Note: not all naturalists are foundationalists.)

Some might hold that since we must start with assumptions, this somehow grants us a freedom to assume whatever we like. However, this is a strawman of the situation. While there are no deductive proofs for naturalistic assumptions, this does not mean that they are accepted without any grounds. In fact, what possible value could there be to an assumption if there were no way to test it? This is the basic error in theistic claims for equity between their assumptions, and naturalistic assumptions.

Let's look at how wrong their claim is:

1) The claim that we must make assumptions in order to begin to know the world would only justifies what is required in order to begin knowing the world.

If, for example, there is in fact a need to assume the existence of other first person ontology other than my own, this assumption only allows me to assume whatever is needed to unpack first person ontology, nothing more.

2) The claim that we must make assumptions in order to begin to know the world would never justify holding to an assumption that fails to adequately account for reality.

This is where pragmatism enters into any foundationalist approach to justifying knowledge. Pragmatic philosopher Nicholas Rescher declares that we are within our epistemic rights to hold to a basic assumption only as long as there is a bilateral feedback loop between assumptions and knowledge. Any claim, such as the future will resemble the past - may be presupposed, as long as the claim is open to revision/falsification. Thus, any assumption we use not only undergirdles attempts to gain knowledge, but must be subject to testing in the very process of gaining knowledge.

The presupposition of 'god' is incapable of being tested, rendering the 'god presupposition' pragmatically meaningless.

3) The claim that we must make assumptions in order to begin to know the world would not justify making any assumption that violated what we know of the world through rational-empirical methods.

Consider Stephen Hawkings here, in his description of speculative cosmological theory:

"There are cosmological models that have as much evidence going for them as astrology. They differ from astrology, however, in that they do not violate what we already know of the universe." - Universe in a Nutshell.

4) The claim that we must make assumptions in order to begin to know the world would not justify any supernatural or 'transcendent' assumption.

Why? Because these terms, "supernatural" and 'transcendent' are defined from the outset, in such a way that they preclude the possibility of holding to them as 'properly basic beliefs' because each definition is a negative definition, devoid of any universe of discourse.

To clarify further:

A negative definition requires a universe of discourse for it to be able to tell us 'anything'. For example, if I hold out a box with two objects, a penny and a pencil and rule out the penny as the object I want to point out to you, the universe of discourse (items in the box) provides you with information concerning what the object in question 'is" - the pencil.

However, a negative definition devoid of any universe of discourse is necessarily meaningless. There's 'nothing' left over for it to 'be', so the definition cannot provide any ontological status. So, to go right to the heart of the matter, to say that the 'supernatural' is the antithesis of nature is to render the concept meaningless.

Review:

So, to review: a naturalist only assumes what is needed in order to active a particular system of thought, she drops any any assumption that is falsified*, she does not assume what appears to contradict what we know of the world, and she never assumes what violates basic ontology itself.

So, in finally answer the question: are these beliefs unjustified, I can say this: Yes, these beliefs are basic and they are unjustified in the epistemological sense in that there is no set of proofs or inductive evidence for them. But the claim that these beliefs are 'unjustified' in the colloquial sense of the word: that there's NO reason to hold to them, they are taken on faith!", is rendered nonsensical.