I always see comments under posts like these with people proclaiming that ASML/europe should just ignore these demands or asking why the US could even make these in the first place but most people just hear about the companies/machines and don't really understand the situation.
First ASML did not really become the sole provider of high end lithography because they were the absolute best or anything its just that they were the last one standing after decades of mergers and acquisitions consolidated the industry to just a single company. So even though they are incorporated in the netherlands and build the machines and do a lot of their work there they rely on lots of engineering work from around the world and very heavily from inside the US from companies that were merged into them.
More important than that though ASML is mostly an engineering/manufacturing company but before it gets to the point of designing and building these machines it requires years to decades of scientific research and the vast majority of that research is done in the US. In some cases it is US corporations like IBM and universities who do a lot of this but also the US government funds/performs a lot of this as well. So many of the early EUV patents are actually owned by the US government and licensed to ASML so going against the wishes of the US govt could risk being cut off from those patents. Even if you think they should just ignore the patents and build them anyway that would still cut them off from future research.
From the perspective of ASML even if they don't like this they really don't have a lot of choice but to do it and it probably does not have a huge short term effect on them financially anyway since they are already booked up for years in advance so they really only miss out on things like service contracts.