Yes, modern society loves its Romeos and Juliets. We forget that in the original play the two lovers died. If he's Orthodox, how will he continue to be observant if he doesn't have kosher food to eat or a shomer shabbos home? Everyone watching the movie thinks he is so darling being orthodox, but the very relationship he is developing will destroy that orthodox observance that they love.
I'm not here to tell people who they can and can't marry. But choices do have consequences (both ways).
First, if he marries her, the status of his children is not clear. For example, Orthodox Jews will say that the children are not Jewish since one is only a Jew if born of a Jewish mom or a convert. The Reform will accept his children as Jews, but only if they are raised as Jews.
The truth is that when Jews intermarry, then tend to compromise in the home. For example, they will allow in the celebration of Christmas and other elements of the Christian religion. It creates confusion for the children. "Am I a Jew or am I a Christian? Is Jesus God or is God echad?" Statistically, children in general raised in homes that are not committed to one religion are more likely to grow up and be a none of the above. Children born to Jewish-Christian interfaith marriages are more likely to not practice Judaism as adults, and to intermarry themselves. The odds are overwhelming that the grandchildren will not self-identify as Jews.
In other words, intermarriage has a tendency to end the Jewish line for that person, if not in all cases, in far too many.
Like I said, I'm not here to boss people around and tell them who to marry. But they should marry with the full knowledge of the likely consequences of their actions.
Now, on the flip side...
Synagogues like mine have basically accepted intermarriage because it is so common. Our goal is to mitigate the damage as much as possible. The question is, how can we save the children?
The answer is outreach to the spouse and Jewish support for the family. Rather than shunning intermarrieds, we go out of our way to embrace them. We make the Gentile spouse feel a part of our Synagogue family. We provide lots and lots of classes in everything from learning Basic Judaism and Hebrew to Challah cooking parties. We never make them feel bad for being Christians, and we answer honestly and with love all their difficult questions -- usually this happens over many many years. There is no rush; after all, it's not like we are after conversions.
I think we are doing a very good job. There seems to be a lot of Shalom in the Home and a high rate of bat and bar mitzvah among the kids, which is what we are after.
Strangely, though it is not our intention in the slightest, we have a very high rate of spouses eventually converting to Judaism. I'd say about 20% of our congregation are converts.