That didn't sound familiar in that book, so I looked it up in several very different translations. The verse doesn't say that, or anything close to that.
Here is the verse from the King James translation:
For without are dogs, and sorcerers, and whoremongers, and murderers, and idolaters, and whosoever loveth and maketh a lie.
It doesn't say anyone cannot inherit eternal life, but lists several groups who have already lost it by not repenting when they could have, including those who practiced one particular sexual sin, not sexual immorality in general, which is condemned elsewhere.
Anyone who repents can inherit eternal life. Don't misrepresent Scriptures.
My comment was a summary of this passage, in which “dogs” is the polite Jewish term for male homosexual prostitute.
The context here is who will be allowed in the New Jerusalem and who will be excluded. The New Jerusalem is only for those people who have repented of their sins and accepted the free, but conditional offer of Jesus (John 3:16). Those who are “outside” are those who are explicitly excluded and will perish. See for example Rev. 21:8.
You are correct in the fact that anyone who satisfies the conditions laid down by Our Lord will receive his free gift of salvation. Revelation 21:8 and many other passages (such as the wheat and tares of Matthew 13) make it clear that some people will refuse to repent.