Yes, the lists were a huge problem.

In places where the germans had access to identity information survival rates among jews was much lower. The Danish government refused to provide data about Jewish citizens to the occupying germans, and simply didn't comply in general with anti Jewish efforts. 99% of Danish jews survived the war.

In the Netherlands, where there was initially a policy of compliance, the occupying germans got their hands on the lists of jews and only 25% of Dutch jews survived.