As we saw after a couple of drones exploded over the Kremlin (somewhat close to the empty stands from where the parade was going to be watched), Russia called it a terrorist attack.
Ukraine denied involvement in the alleged strike. [...]
The Kremlin Press Service has called the purported drone attack an “attempt on the President’s life,” said it was an “act of terrorism” and blamed Ukraine. [...]
In his response to the attack, Russian State Duma Speaker Vyacheslav Volodin called for the use of weapons capable of “stopping and destroying the Kyiv terrorist regime.”
So it doesn't matter too much what international law says about any of this, as far as Russian response is concerned. A few nights later they launched 30-something 'Shaheds' (I forgot the Russian name for that) and a similar number of cruise+ballistic missiles at Kyiv, according to Ukraine. But overall these numbers don't seem unusual, e.g. compared to March, when Russia claimed it was responding to a ground incursion by Ukrainians killing civilians in the Bryansk region (one of the areas from where Ukraine says Shaheds are launched).
As far as Western reponse goes, many expressed skepticism about the Russian claims about the drone attack on the Kremlin, while the other kind of events, like [claims of] ground infiltrations receive little attention in the Western press. (Also, Russia even claimed the Kremlin drone explosions were “dictated” in Washington, a claim strongly denied by the US.)
Just in general terms, while the White House said (previous source) it "is certainly not encouraging or enabling Ukraine to strike beyond its borders", the UK MoD said (last year) that "It is completely legitimate for Ukraine to be targeting in Russia's depth in order to disrupt the logistics, that if they weren't disrupted would directly contribute to death and carnage on Ukrainian soil." So that's the political rather than the legal limit that Ukraine has to deal with.
As far as the  Moscow parade goes, for various reasons, Russia has reduced the amount modern weaponry involved to practically nothing this year. Apparently the only tank displayed was a single (WW2 vintage) T-34. (This is in contrast with 2021, for example, when dozens of modern tanks were showcased.) The personnel involved in the 2023 parade was also reduced, and "the majority were auxiliary, paramilitary forces, and cadets from military training establishments [... while] the only personnel from deployable formations of regular forces were contingents of Railway Troops and military police.” (according to one Western source). So, legally perhaps still a valid target, but substantially more difficult politically than if e.g. columns of modern tanks were still involved.