Any path toward support of the ICC will require examining long-standing concerns about the exposure of U.S. military service personnel and American political and military leaders to the court, whether or not the United States is a state party to the Rome Statute.Are not U.S. military personnel subject to the laws of foreign states that they visit?
At least someone elected the British Parliament. Nobody elected the ICC.
Yes, they are, as subject to the treaties with the countries they are serving in.
Why is the idea of U.S. military personnel being subject to the ICC more controversial than them being subject to the laws of the British Parliament?
This is because countries with malaise towards the US like Iran, China, Russia, and North Korea could use the ICC to bring up false charges against US servicemembers and politicians.