Question: When Jesus Christ speaks to Joseph Smith in the 1832 First Vision account, did He say that one receives eternal life regardless of what church they are affiliated with?

The Lord does not state in the 1832 narrative that eternal life is available to members of every Christian church

all those who believe on my name may have Eternal life behold the world lieth in Sin...

—Joseph Smith's 1832 account of the First Vision

In light of the statements produced by Joseph Smith before he wrote the 1832 quotation of Jesus Christ in the Sacred Grove, it is not possible to uphold the claim that the Lord told the Prophet on that occasion that a Christian of any denomination automatically qualified for eternal life (in the LDS understanding of the term).

While it is true that the Lord is quoted in the 1832 First Vision account as saying "all those who believe on my name may have eternal life" it can be seen in an earlier revelation dated 7 March 1831 that those who "believe on [Christ's] name" must also "come unto [Him]" in order to "have everlasting life" (DC 45:5).

The Lord does not state in the 1832 narrative that eternal life is available to members of every Christian church. Rather, He declares unambiguously in that account that "none" of the existing Christian denominations of the time were keeping His commandments; they had all turned aside from His gospel. From this piece of information alone, it is clear that eternal life could not be made available to them; they were categorized by the Lord as being in a state of "sin" (cf. Romans 5:21; Romans 6:22-23). In the 1832 text Jesus Christ says to Joseph Smith - "keep my commandments," and in connection with this it can be seen in a revelation dated March 1829 that the Lord informed the Prophet that he could only be granted "eternal life" if he was "firm in keeping the commandments" that Christ gave unto him (DC 5:21-22; cf. DC 14:7; DC 18:8; DC 30:8).

On 1 November 1831 the Lord affirmed to adherents of the LDS faith that there was "only [one] true and living church upon the face of the whole earth" (DC 1:30). Earlier—in May 1831—He had spoken specifically to members of "the church that profess my name" (compare with the 1832 document wording) and indicated that only the faithful members of it who endured would "inherit eternal life" (DC 50:4-5). Thus, the blessing of eternal life could not be obtained without complying with certain conditions.

Before Joseph Smith penned the Lord's words that are found in the 1832 First Vision text he clearly understood that:

Profession of the Lord's name alone is not sufficient for the reception of eternal life; a person must also "come unto" Him.
Eternal life is granted only to those people who keep the Lord's commandments.
One of the Lord's commandments is to be baptized by, and receive the gift of the Holy Ghost through His authorized representatives (DC 49:11-14 / March 1831; DC 76:51-52 / 16 February 1832).
There is only one church on the earth that is recognized by Jesus Christ as being His own.

The implication of this last point is that only one church can perform ordinances that will be considered valid in the sight of the Lord. And so a person can only be truly obedient to all of the Lord's commandments by holding membership in His one true Church. Joseph Smith indicated in the introductory remarks of the 1832 history that he had received priesthood authority, from a heavenly source, which enabled him to "administer . . . the commandments . . . and the ordinances".

Notes

Question: When Jesus Christ speaks to Joseph Smith in the 1832 First Vision account, did He say that one receives eternal life regardless of what church they are affiliated with?