They’re considered invasive in many areas, but native birds in the US (and presumably elsewhere) do eat the seeds:
In Florida they’ve been documented as a pollen source for native and non-native bees:
There are many species all across South to East Asia (about 50 species), and in India one of the species is important for the Antheraea paphia moth, which is a local silk producing species.
In Vietnam they’re important habitat for a range of moths and butterflies, both as larvae and adults.
Some species of Crape-Myrtle, such as Lagerstroemia minuticarpa, are endangered (Critically Endangered in this case)