I think there is a much deeper question under the surface of this question. It is one of world view. The question is should we take a Christian world view of raising children, or a secular one.
In the Christian world view, God created them Male and Female. Gender is determined at conception. Males have XY Chromosomes and Females have XX Chromosomes. The Chromosomes cannot be changed and the Gender cannot be changed. You can take a male with XY Chromosomes and pump him full of hormones, do some surgery, and he still has XY Chromosomes and is still a male. In the Christian world view, you do not get the choice of gender, but it is decided by procreation. In other words, in the Christian world view, you cannot argue with Chromosomes. In a Christian world view, the concept of changing gender is a violation of basic and obvious moral issues and rebellion against creation, and against God. The issue is one of divine law and obedience to God. A Christian parent would have concerns about a boy cross dressing and might view that as a potential moral issue.
In the secular world view there is confusion about what gender a person actually might be, because gender is based upon individual choice. The secular world view does not base gender on mere biology. In the secular world view, there are no spiritual issues, and only the material counts, and there is no truth beyond the natural material world. In the secular world view, gender change is a matter of choice and there is no such thing as divine law, and accountability to God for moral issues. In fact, morality is generally subjective. Truth is also subjective. So then, truth and morality can be based upon the subjective choices people make. The concept of a boy cross dressing is then one of preference for the boy. So then, if boy chooses to be a girl one day, then that is a good thing because it is based upon choice. But if in the future, the boy decides to go back to being a boy, that does not mean the first choice is wrong, in fact there is not such thing as a wrong choice. Concepts of right and wrong become very blurry.
(The only objective truth is that all truth is subjective--- except for the objective truth that truth is subjective--- sounds confusing??? yes, because it is total confusion).
THE QUESTION IN THE OP:
When you wrote ....
"I don't really know what to do. I don't want to overreact. Some of his friends' parents are pretty liberal too and I don't want them to go "poor kid with his crazy fundie dad". What's the moral thing to do here? Should I stamp out this behaviour and insist on God's word on this or just let it be and hope it's just a passing phase?"
That raised questions. Why are you so afraid of being called a name? I am not really a fundamentalist, I consider my tag to me "evangelical." Yet if I were called a name like "fundie" I hope I would respond by telling them I am a double super duper fundy if your messing with my son.
My impulse might be one of two ways.
1------to let the kid alone, it is not his fault. Also, it could all be innocent. It is possible even the other parents had nothing to do with this. Its just not an issue. If they did not use your son for their own purposes, then be careful not to make a false accusation. Then you will be in the wrong. It could have been something innocent. I do not know and cannot tell. As far as your son, hey, he is 7. Give the kid a break. He is probably innocent of everything. A little nudge in the right direction might be worth it. I might mention to him that "I am glad you like being a boy because God made you a boy."
2------On the other hand, the other parents could be behind this. But if the other parents are using your son to subvert your Christian world view, then I hope you have the spine to hold the hill down to the last man and the last bullet (speaking figurative of course!!). The point is then, have a spine!!! More than your son is at stake, your own identity as a Christian parent is at stake. It would actually be great if they call you a few names, then you know where they are. Any weenie that would use your son to subvert your world view is no friend, but a snake in the grass. I intentionally use the word "weenie" because these other parents did not have the backbone to talk to you about the issue. Anyone that would use your son that way is dangerous, and you had better be cautious.