My problem with the name is that leftists/Marxists have used WWII and the Holocaust as a framework for fighting against any group right of center politically and/or socially.
Marxists thought post Hitler has been focused on "deconstructing" all facets of society that they believe are dangerous or contributed to the rise of Hitler. For instance, the nuclear family, border security, sexuality, and all conservative social/political ideals have been demonized because they "lead to Hitler" in one way or another.
I do not know why exactly they want this named changed. Maybe they just indiscriminately hate Jews, anyone they consider white, or Germans in general. If that is the case, then they are wrong. However, I would not be surprised if the workers at this daycare center are extremely liberal are using Anne Frank and the Holocaust to push their Marxist agenda onto impressionable children.
"The nuclear family is a problem because it led to Hitler and Hitler killed Anne Frank."
"Hitler repressed the LGBT, so we need to support it because repression led to Hitler and he killed Anne Frank"
"You don't want to be like Hitler do you? He killed Anne Frank"
I do not think this scenario is outside the realm of possibility. Many migrant children are going to be coming from much more socially conservative backgrounds and they will reflect what they learn from their parents. Many liberal teachers take it as their personal mission to "undo" these beliefs in children they are in charge of.