No, it doesn't. We don't know what the forbidden fruit was, and nowhere does the Bible say it was an apple. Even if it had been, that wouldn't be a reason to avoid apples today. The writer of the Song of Solomon compared the joy of married love to "an apple tree.... sweet to my taste" (Song of Solomon 2:3).
The important thing isn't what kind of fruit it was, but why Adam and Eve were told to avoid it. The reason was because it gave them a choice -- either to love God and obey Him, or to reject Him and disobey Him. If they hadn't had a choice, they would have been like puppets, and their love for God wouldn't have been genuine.
But they did have a choice -- and at first they loved God and walked with Him every day. Then Satan tempted them in the strongest possible way, telling them that God had been lying to them, and if they ate the forbidden fruit they would become like God. They fell for his lie -- with catastrophic results.
Today Satan also tries to get us to believe a lie -- the lie that God hates us, and that there can be no forgiveness or salvation. But there can be -- because God sent His Son, Jesus Christ, into the world to save us by His death and resurrection. The Bible says, "For as in Adam all die, so in Christ all will be made alive" (1 Corinthians 15:22). Is your faith and hope in Him?