if I add a mod, the Anchors are getting different textures:

might be caused by this feature:
Put a block in your offhand and right click a Travel Anchor with an empty main hand to disguise it as that block
But: its not a normal behavior to change the texture if the mod-set changes. So maybe there is truly something wrong with the rendering of the blocks?

every time I am adding or removing a mod, I can reconfigure all my anchors with the correct block, it is very annoing.

sometimes it does not render the block which is defined in its NBT Data. But I am not able to find out why.