With the mod:

Without the mod:

Issue likely stems from the triangulator combined with NTM's own rendering for connected texture blocks, NTM is open source and the connected texture-related rendering is all found here: https://github.com/HbmMods/Hbm-s-Nuclear-Tech-GIT/tree/master/src/main/java/com/hbm/render/block/ct

Was a solution to this ever discovered?
With the release of the NTM Space fork, I'm planning to run it on my server with friends, but losing FalseTweaks would be a big blow.

I don't know if it helps, but it looks like this now:

Also try adding com.hbm.render.block.* to the TESSELLATOR_USE_REPLACEMENT_TARGETS list in falsetweaks.cfg

I built a jar with some patches that i tested against NTM 1.0.27_X5027, please check if this works:
https://mvn.falsepattern.com/releases/com/falsepattern/falsetweaks-mc1.7.10/3.1.0-4-gb80d5fc/falsetweaks-mc1.7.10-3.1.0-4-gb80d5fc.jar

Try turning off the quad triangulation setting and see if that fixes it.

Sorry, I only just woke up.
I see that the Modrinth version was updated after you sent this, does that include the fixes?

I haven't tried it yet, but quad triangulation seemed to be off by default (ENABLE_QUAD_TRIANGULATION).
If the new version doesn't work, I'll try the tesselator target thing.

Fixed in 3.x