I believe no US administration ever acknowledged the ICC. By the way, the German chancellor just said he wouldn't arrest Netanyahu if he came to Germany.
If there is a nation that cannot be expected to act with equanimity in regards to Israel, that's Germany. Nothing to do with the legitimacy of the ICC, that Germany has always recognised.
In most countries state prosecutors are directly controlled by the executive. The US is a bit of an anomaly in having semi-independent elected prosecutors. The government wouldn’t normally get directly involved - the optics are terrible - but in high profile political cases they will.
It's not just a Trump thing.