John of Japan said:
The "one mention" of false prophets occurs in v. 15. This sets the context for the verses on fruit. From v. 15 to v. 20, the pronouns "they" and "them" them must, gramatically, refer to the false prophets of v. 15. There is no other possibility in either the grammar of the English Bible or Greek NT grammar. Anytime you start interpreting Scripture out of context you have started down the proverbial "slippery slope," and can end up in false doctrine. Beware.
The problem with your interpretation is that Jesus throughout his ministry taught the necessity of following Him with regard to salvation. It's not an argument about one verse, it's a position on the whole of Jesus' ministry.
And when de described the Judgment in MA 25 it was very clear.
Mat 25:31 When the Son of man shall come in his glory, and all the holy angels with him, then shall he sit upon the throne of his glory:
Mat 25:32 And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth [his] sheep from the goats:
Mat 25:33 And he shall set the sheep on his right hand, but the goats on the left.
Mat 25:34 Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
Mat 25:35 For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in:
Mat 25:36 Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me.
Mat 25:37 Then shall the righteous answer him, saying, Lord, when saw we thee an hungred, and fed [thee]? or thirsty, and gave [thee] drink?
Mat 25:38 When saw we thee a stranger, and took [thee] in? or naked, and clothed [thee]?
Mat 25:39 Or when saw we thee sick, or in prison, and came unto thee?
Mat 25:40 And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done [it] unto one of the least of these my brethren, ye have done [it] unto me.
I know you'll want to call this the "Bema Seat Judgment" and claim it's all about rewards and doesn't refer to eternal salvation but I don't see THAT in the scripture.