Among Orthodox Jews, the trend is not to date recreationally. Dating is usually done solely for the purpose of finding a matrimonial partner. As such, most Orthodox Jews don’t begin dating until they are in the 18-22 range (of course, when someone is ready to get married varies from person-to-person).
As such, when my children are of that age, I doubt that I will have the “power” to forbid them to not date any particular person.
However, it is still of supreme importance to us that our children marry Jews and no one else. It doesn’t make a difference to me if they are American, Israeli, Italian, Mexican, Polish, black, yellow or purple-with-orange-stripes-and-green-polka-dots. What matters to us (my wife and myself) is that our children raise their families and children in a manner that is consistent with Torah Law and live according to Judaism and its precepts.
To do so in an intermarried household is downright difficult, if not outright impossible. Some (Christian/Jewish, as an example) intermarried families raise their children with no religion. Some raise their kids as Christians. Some raise them as Jews. And some with a blend of religions and traditions. I find (from an Orthodox Jewish POV) all of these options troubling.
The thought that my grandchildren might be raised with no religion or as Christians would devestate my wife and myself. Obviously, when the goal is to see that one’s children, grandchildren and great-grandchildren grow up as Torah-observant Jews, this represents the ultimate failure.
Even if they are raised as Jews (assuming, of course, that it is the mother who is Jewish [if not, the kids aren’t Jewish anyway]), they would likely be raised in an environment where the mitzvos (commandments) are not being kept - where the food served is not kosher, where Shabbos is not observed, etc. In addition, you’d have the awkward situations where one parent would have to explain to the other why they do things that don’t apply to them. For example, the Christian parent may pray to Jesus for forgivness. The child would observe this. Would the Christian parent allow the child to do so as well? Wouldn’t that violate the “rule” that they are raising the child as Jewish? What if the child wants to pray to Jesus for forgivness for sins? Or does the parent tell the child that praying to Jesus for forgivness is only appropriate for Christians? If so, wouldn’t the child ask why s/he isn’t a Christian and doesn’t have these rituals?
Raising them in a home where the religions and traditions are blended is also a troubling prospect. How can one (seriously) go to a synagouge on Yom Kippur and ask for forgivness for your sins from the past year and at the same time, profess a belief in a Son of God who died on the Cross to forgive the sins of mankind? How can one go to church on Easter to celebrate the Resurrection of the Messiah while at the same time state that one is still waiting for the messiah to arrive.
My goal (and my wife’s) is to instill in our children a love of Judiasm and it’s precepts; such as that their life’s goals will be our life’s goals - to see that the Torah is observed in their families and that the traditions and values contained therein are passed down to their children and their grandchildren. And to do so in an intermarried home is simply impossible.
So, to bring this back to the beginning of my post - no I wouldn’t “forbid” my child to see someone who wasn’t Jewish - it probably wouldn’t be in my power at the age that they begin dating anyway. But I would voice my disapproval (privately) to my child if they did date someone who didn’t share a commitment to living a life as the Torah dictates.
I know that this may seem harsh to some and seem like I’m issuing an indictment against couples who are intermarried. While the former may be true (Judaism isn’t a convenience, it’s a total life-long commitment) the latter isn’t so. I’m not here to tell anyone else (Jewish or non-Jewish) how they should raise thier children - I’m simply giving my answer to the question as raised in the OP.
Zev Steinhardt