Realistically, it isolates the US and israel even more.
Netanyahu can't go to any countries that are part of the ICC; he'll be arrested on the spot. Same as Putin.
You'll see both Republicans and Democrats criticize this move because their AIPAC handlers have pre-written statements for them.
It will read something along the lines of "antisemitic abuse of law", "blood libel", or just brazen threats on the ICC lawyers.
That's the practical angle.
The optimistic angle is that the West now has a reason to bush Israel and will take full advantage
The pessimistic angle is the West doubles down on its hypocrisy and wholesale denounces international law in defence of Israel