No, this analogy is not true, even slightly — it is a loose and largely inaccurate metaphorical mapping that does not hold up under scrutiny in epistemology or philosophy of religion.

Brief Overview of the Epistemic Positions

These terms come from responses to the epistemic regress problem (how to justify beliefs without vicious circularity, infinite regress, or arbitrariness):

• Foundationalism — Some beliefs are basic (non-inferentially justified, e.g., via perception, self-evidence, or direct awareness) and serve as the foundation for all others. Justification stops at these basics.
• Coherentism — Justification is holistic: beliefs are justified by mutual support in a coherent web or system (no strict foundations or infinite chains).
• Infinitism — Justification requires an infinite, non-repeating chain of reasons (rarely defended, as finite minds can't traverse infinite regresses).

Why the Analogy Fails

1. Foundationalism ≈ Theism This has some slight metaphorical appeal. Reformed Epistemology (e.g., Alvin Plantinga) argues that belief in God can be properly basic — non-inferentially justified (like perceptual beliefs or belief in other minds), without needing evidential arguments. This is a modest foundationalism applied to theism. However, it is not a general equivalence. Many theists rely on inferential arguments (cosmological, ontological), which are non-foundationalist. Classical foundationalism often ties to empiricism or rationalism, not necessarily theism. The analogy is limited to specific theistic epistemologies, not foundationalism broadly.
2. Atheism ≈ Coherentism This is weak or nonexistent. Atheism (lack of belief in gods) does not inherently favor coherentism. Many atheists are empiricists or evidentialists, often aligning with modest foundationalism (e.g., basic perceptual beliefs as foundations, with atheism justified inferentially from lack of evidence). Coherentism is neutral on God — it could support theistic or atheistic belief systems if coherent. No major linkage exists in literature between atheism/secularism and coherentism specifically.
3. Infinitism ≈ Strong Agnosticism This is basically unfounded. Infinitism is a niche view in epistemology (defended by philosophers like Peter Klein), emphasizing endless reasons. Strong agnosticism (God's existence is permanently unknowable) does not map to infinite justification chains. Agnosticism often stems from evidentialism (insufficient evidence) or skepticism, not infinitism. No sources connect the two meaningfully.

Overall, these epistemic theories are general structures for justifying any belief (scientific, moral, perceptual, etc.), not tailored to theism/atheism/agnosticism debates. The proposed equivalences appear to be a creative but unsupported analogy — perhaps inspired by Reformed Epistemology's use of foundationalism for theism — but they do not reflect standard philosophical positions. Theism and atheism both appear across foundationalist, coherentist, and other frameworks.

If this analogy comes from a specific source (e.g., a blog, book, or forum post), it is likely idiosyncratic rather than established. In mainstream epistemology and philosophy of religion, it does not hold.