There is a federal law, 18 USC 2252, which criminalized distribution and receiving of child porn. One part of the law addresses a person who
(1) knowingly transports or ships using any means or facility of
interstate or foreign commerce or in or affecting interstate or
foreign commerce by any means including by computer or mails, any
visual depiction, if— (A) the producing of such visual depiction
involves the use of a minor engaging in sexually explicit conduct; and
(B) such visual depiction is of such conduct;
The next part addresses one who
(2) knowingly receives, or distributes, any visual depiction using any
means or facility of interstate or foreign commerce or that has been
mailed, or has been shipped or transported in or affecting interstate
or foreign commerce, or which contains materials which have been
mailed or so shipped or transported, by any means including by
computer, or knowingly reproduces any visual depiction for
distribution using any means or facility of interstate or foreign
commerce or in or affecting interstate or foreign commerce or through
the mails, if— (A) the producing of such visual depiction involves the
use of a minor engaging in sexually explicit conduct; and (B) such
visual depiction is of such conduct;
The word "knowingly" is crucial here: it may mean that if you don't know, it's not a crime. The wording is not completely clear, in that maybe the law only says that you have to know that you received and don't have to know anything about the item that you received. So it is up the the Supreme Court to say exactly what that means. In US v. X-Citement Video, Inc., 513 U.S. 64, they did. The court held that "knowingly" does not just mean that you know you are receiving or distributing, because that would yield absurd results such as that a retail druggist who returned a roll of film unprocessed would be guilty of distributing child porn, just in case the film contains child porn. As the court says, "We do not assume that Congress, in passing laws, intended such results".
There is a general constitutional presumption that any crime has a scienter requirement (Morissette v. United States, 342 U. S. 246, Staples v. United States, 511 U. S. 600): "the standard presumption in favor of a scienter requirement should apply to each of the statutory elements that criminalize otherwise innocent conduct". The court rejects the narrow interpretation that "knowingly" just applies to the verb, and "This interpretation is supported by the canon that a statute is to be construed where fairly possible so as to avoid substantial constitutional questions".
There are also state laws which are untouched by X-Citement, which may make possession of child porn a strict liability offense. Washington state law is written so that you have to know or intend ("Knowingly develops, duplicates, publishes, prints, disseminates, exchanges, finances, attempts to finance, or sells a visual or printed matter that depicts a minor engaged in an act of sexually explicit conduct as defined in RCW 9.68A.011(4) (a) through (e)" or "Possesses with intent to develop, duplicate, publish, print, disseminate, exchange, or sell any visual or printed matter that depicts a minor engaged in an act of sexually explicit conduct as defined in RCW 9.68A.011(4) (a) through (e)".)
The statutory rape law on the other hand has no requirement pertaining to knowledge or intent
(1) A person is guilty of rape of a child in the third degree when the
person has sexual intercourse with another who is at least fourteen
years old but less than sixteen years old and not married to the
perpetrator and the perpetrator is at least forty-eight months older
than the victim.
I don't know whether some state's statute was written without a "knowingly" requirement.