Robert Frost is not the kind of poet to insert religious imagery into his poems. A subtle Christian allusion is rare. However, the poet writes a lot of meditations on life and death, so that always brings in spiritual questions. In "Birches," Frost mentions "heaven" twice. Notice how it is always with a lower-case h and is more suggestive of the sky than paradise. The poem could be read as an allegory, but it's a little too skeptical for that.
The speaker uses "Truth" ironically to express his skepticism of all belief (including science).
The speaker uses some images that could be seen as religious, but expresses them in such a vague way that a reader can't turn "Birches" into a religious allegory.