Child pornography laws vary between the federal and state government, and then from state to state, as well. At the federal level, the 1968 version would not constitute child pornography.
Under 18 USC 2256, child pornography only includes depictions of minors (under the age of 18) engaged in actual or simulated "sexually explicit conduct," which is defined to include only:
(i) sexual intercourse, including genital-genital, oral-genital, anal-genital, or oral-anal, whether between persons of the same or opposite sex;
(ii) bestiality;
(iii) masturbation;
(iv) sadistic or masochistic abuse; or
(v) lascivious exhibition of the anus, genitals, or pubic area of any person;
I don't see a good argument that the film meets any of those criteria.
I'd call it unlikely that the film meets the criteria for child pornography under any state law. I don't believe I've ever seen such a law that both (1) goes beyond prohibiting depictions of sexual conduct to mere depictions of nudity; and (2) contains no exceptions for material with serious literary, artistic, political, or scientific value in hopes of avoiding First Amendment problems.
This is not to say that such a law does not exist or that such a law would be unconstitutional under the First Amendment.
In New York v. Ferber, 458 U.S. 747 (1982), a defendant who sold videos depicting young boys masturbating was convicted under New York's child-pornography laws, which imposed felony penalties on anyone who "produces, directs or promotes any performance which includes sexual conduct by a child less than sixteen years of age." New York's appellate courts overturned his conviction, holding that even if Ferber's videos were not protected by the First Amendment, the entire child pornography law was unconstitutional because it would not protect materials that "deal with adolescent sex in a realistic but nonobscene manner." But the U.S. Supreme Court reversed and reinstated the conviction, rejecting Ferber's argument that the First Amendment required such accommodations:
While some States may find that this approach properly accommodates its interests, it does not follow that the First Amendment prohibits a State from going further. [This] standard, like all general definitions of what may be banned as obscene, does not reflect the State's particular and more compelling interest in prosecuting those who promote the sexual exploitation of children. Thus, the question ... of whether a work, taken as a whole, appeals to the prurient interest of the average person bears no connection to the issue of whether a child has been physically or psychologically harmed in the production of the work. Similarly, a sexually explicit depiction need not be "patently offensive" in order to have required the sexual exploitation of a child for its production.
One might therefore write a law broadly enough to include the 1968 version of Romeo and Juliet within the definition of child pornography. For instance: "It is illegal to create, possess, or distribute child pornography. "Child pornography" means any visual depiction of (1) a minor engaged in sexual conduct; or (b) a minor's breasts, genitals, or buttocks."
There would still be plenty of room to argue about whether it was constitutional, primarily because the state's interest in protecting minors from sexual exploitation is less obviously implicated by a film depicting minors kissing or walking around naked than by a film depicting them engaged in actual sexual conduct.
But if that law did survive a First Amendment challenge, Romeo and Juliet would likely become illegal. Virtually all of the objections raised in the various comments throughout this post would be legally irrelevant, as it would not matter where the film was made, when it was made, whether the children were above the age of consent, whether the actors lied about their ages, that the actors were only partially nude, that the film doesn't meet the standard for obscenity, that the film has serious artistic value, or that the actors suffered no actual injury from participating.
The only things that would matter would (1) whether the film depicts a minor's breasts, genitals, buttocks, or sexual activity; and (2) whether you have created, possessed, or distributed that film.