I refrained from following up earlier because I was unfamiliar with the verse in which the phrases "sexual immorality" and "unnatural lusts" occurred together. Thank you for providing the reference.
But how gullible do you think we are? Or perhaps the question should be "how gullible are you?" You present a pairing of verses that only appear in one translation -- a dynamic translation at that -- and in only in one verse, as a pairing that must mean that together they signify homosexuality.
Let's take a closer look at that verse:
ως σοδομα και γομορρα και αι περι αυτας πολεις τον ομοιον τροπον τουτοις εκπορνευσασαι και απελθουσαι οπισω σαρκος ετερας προκεινται δειγμα πυρος αιωνιου δικην υπεχουσαι
(The Westcott-Hort edition of 1881)
as Sodom and Gomorrah, and the cities around them, in like manner to these, having given themselves to whoredom, and gone after other flesh, have been set before -- an example, of fire age-during, justice suffering.
(Young's Literal Translation)
Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire. (KJV)
Just as Sodom and Gomorrah and the cities around them, since they in the same way as these indulged in gross immorality and went after strange flesh, are exhibited as an example in undergoing the punishment of eternal fire. (NASB)
Even as Sodom and Gomorrah, and the cities around them, having, in the same way as these, given themselves over to sexual immorality and gone after strange flesh, are set forth as an example, suffering the punishment of eternal fire.
The word unnatural (or rather the Greek phrase usually translated as unnatural, against nature, etc) does not appear any where in this verse. Instead, as in the more literal translations I have provided, it is the phrase "heteras sarkos" which the translators of the RSV chose to render -- dynamiically -- as "unnatural lust."
Both the idea of sexual immorality and the men going after (not lusting after) "strange flesh" come from the Book of Jubilees, as I mentioned above, and they are not the same idea, and neither indicates that the men of Sodom were homosexuals.
You can't base your theology on a single translation of the Bible, especially a dynamic one. You are too much at the mercy of the whims of the translators.