This issue is only present on the latest version of Abnormals Core.
To avoid it, keep using version 3.1.1

There was an internal change made to Abnormals Core's signs, and some mods were using the signs in a way we were not expecting, leading to issues happening with some other mods in the latest version.

FYI

This issue seems to be raised with version 3.2.0 of Abnormals Core (looking at the date).
It is still persisting with 3.3.0 as of 2021-10-09.
One still has to revert to 3.1.1 if the game won't start and you find the following in your crash report:

java.lang.NoClassDefFoundError: com/minecraftabnormals/abnormals_core/common/items/AbnormalsSignItem

FYI

This issue seems to be raised with version 3.2.0 of Abnormals Core (looking at the date). It is still persisting with 3.3.0 as of 2021-10-09. One still has to revert to 3.1.1 if the game won't start and you find the following in your crash report:

java.lang.NoClassDefFoundError: com/minecraftabnormals/abnormals_core/common/items/AbnormalsSignItem

Yes, this is true, which is why this issue is still open.
Fixing this issue in 1.16.5 would break even more mods using the sign system.
This issue will get closed when Abnormals Core releases for 1.17.

This issue no longer occurs in 1.17+ versions of Blueprint.