What, exactly, is nature? Is humanity not part of it?
If you define nature as those things not influenced by humanity, well, life would not be pleasant if everything were natural. The clothes you wear, the home you live in, the computer you are communicating with, none of these are natural. The medicines with which we fight disease heal injuries are not natural. Hell, cooking food is not natural.
Besides, there's no way to know if a person who has gender identity issues would survive and pass along their genes in a purely 'natural' world.
Human nature vs. Nature is an entirely different discussion.
As far as your last statement goes, we can be fairly certain that someone with gender identity issues is far less likely to pass its genes on to subsequent generations based solely on the un-natural condition in the first place.
Let's just apply that to the case featured in the OP:
Little boy's parents have managed to persuade the child that he is really a little girl. He's got all the boy bits, but mom and dad have twisted his little mind into something Nature never intended. So, it goes through life as a "girl". When it comes time to start dating, do you think it will develop romantic and sexual interest in males or females? Remember, the boy bits are disregarded, even hated, by this child.
If it develops an interest in boys, as would be normal for a girl-child, do you think the boys are going to be all the interested in it once they learn its dirty little secret? Maybe boys who have identified as homosexual, but normal hetero boys might find the extra appendage...off-putting. Regardless, boy-on-boy sex engenders no offspring.
If it develops an interest in girls, do you think normal girls will be interested in dating a boy who looks better in their clothes than they do? Considering the attitude this child has towards its 'masculine' member, would it consider heterosexual relations with another girl? Perhaps a chance of offspring, but not very likely.
If it mutilates itself to become "female", it may have sexual relations with other (unsuspecting) males, but there will still be no issue.
So what do you think? Much chance of passing those genes on to offspring? IF this were a genetic anomaly. Klinefelter's Syndrome is one of extremely few genetic anomalies I am aware of that might result in gender identity issues, and Klinefelter's renders its victims infertile. Hermaphroditism is another genetic anomaly that might render the victim 'confused' about their gender identity.