I agree with you, also as an american. I want to blame 'our' fear of nudity and sex on the Puritans and our puritanical (ha) national religious views. Love of violence or acceptance of violence feels like the reciprocal impact of fear of sex.
The idea I have is our fear of sex lead to US film makers searching for something that would get people's attention, and violence turned out to be it. One could also make a vague claim about guns being a more natural part of our independent fantastical claims of living on the frontier (needed to kill the previous inhabitants during our genocidal takeovers). But I think it was the infamous Hayes Code (https://en.wikipedia.org/wiki/Motion_Picture_Production_Code) in the 1930s, where we moved from a time without as much cinematic censorship (that allowed both violence and sex & nudity at times) into a time that was much more anti-sex in the media. The anti-sex was already there, but the Hayes code gave anti-sex conservatives much more power to control mass media for a while.
I think both the American cultural fear/disgust of sex and acceptance/romanticizing of violence both come from the same Judeo-Christian roots. The Bible often describes violence as part of God's justice, and this idea of just violence is expressed everywhere from chivalric codes and ideals of masculine/gentlemanly behavior to the very concept of states as monopolies on violence and policing.
Even setting that aside, you have the influence on Western culture of Greek and Roman myths, where heroes were defined not by recognizably Christian moral virtues but by their superhuman capacity to commit violence. The ancients weren't particularly afraid of sex either (nor did they have the same ideas about sexuality that would develop into the heterosexual/homosexual dynamic in Christendom) but it's easy to see how the aspects synchronous to the Judeo-Christian ideal would persist in the culture while the other stuff went by the wayside.
The idea I have is our fear of sex lead to US film makers searching for something that would get people's attention, and violence turned out to be it. One could also make a vague claim about guns being a more natural part of our independent fantastical claims of living on the frontier (needed to kill the previous inhabitants during our genocidal takeovers). But I think it was the infamous Hayes Code (https://en.wikipedia.org/wiki/Motion_Picture_Production_Code) in the 1930s, where we moved from a time without as much cinematic censorship (that allowed both violence and sex & nudity at times) into a time that was much more anti-sex in the media. The anti-sex was already there, but the Hayes code gave anti-sex conservatives much more power to control mass media for a while.