All banks have to comply with Know Your Customer regulations, which is easier for bigger banks than smaller ones. And yet society has deemed that combating money laundering and tax evasion is worth the cost. It'll be fine. Just raise more capital from your investors, it's essentially free these days.
The more interesting story with this law is more of a meta story. Here we have a change to a bedrock law that for over 20 years has granted the tech industry immunity from any liability for anything on their platforms. Which is just kind of amazing if you think about it. Imagine if the energy industry didn't have to deal with EPA regulations or manufacturing companies didn't have to deal with OSHA regulations. The political winds are starting to shift and the tech industry is increasingly going to be held responsible for the negative externalities they create.