I am opening another issue for this because when it was reported to sinytra they said it could not be fixed on their side. https://github.com/Sinytra/Connector/issues/1001
Now that you know the cause is this something that can be fixed?

This issue also happens with athena, it is unrelated to sinytra its just that continuity is not on forge natively.

Sinytra/Connector#1001

This appears to be a conflict between the two mods. if I recall correctly, blueprint replaces minecraft's resource manager with its own, as well as making several other changes to the model system, which eventually cause continuity to stop working. Unfortunately, this cannot be fixed on our side.

Already posted similar issue #240 a while ago, but it was closed

Yes, I opened this one and checked sinytra because I saw yours and followed the trail.

Is reproduceable on my end as well

For me it causes a crash when the mods are together

yes, please fix it! this mod is required for other mods that I have

when is this stupid incompatibility gonna be fixed? 😤

Can confirm it is also happening to me on forge 1.20.1

Can confirm

https://www.curseforge.com/minecraft/mc-mods/blueprint-texture-issue-fix
fix mod here