It is wrong and unloving to ever think that John 3.16 teaches that all you have to have is the right doctrine in your head and you will be saved. “Whoever believes” actually has a very different meaning depending on whether you think the Bible is God-centered or man-centered. “Whoever” does not mean “anyone”; in this verse it means “every one.” In fact it is literally “every believing one.” “God loved the world in such a way that he gave his only Son, that every [single] one who believes in him, will not perish but have eternal life.” John 3.16 is a promise, not an invitation.
And “believes” does not mean “thinks rightly.” It means “trusts”. Lots of people think rightly about Jesus. Just as many will say “Lord, Lord,” many will also say “I believed in you.” Let us not be so quick to pronounce salvation on those who say they believe if they show little evidence of the new birth. And the best evidence of the new birth is that they always change whenever the truth is presented in love to them. Always.
If we cannot even get John 3.16 right, what hope have we for a lost and dying world?