Beginner's question: UV mapping / straighten the islands with polygons possible?

I’ve created a basic stone wall with a cube, added some loop cuts and bevels for the edges. Scaling is applied. And then I marked some seams (1 in the image)

When I unwrap I get the following UV: (2 in the image)

The problem is that I want the islands to be straight as otherwise the stones from the textures are misaligned on the wall. I want the “lines” from the stones of the texture follow the lines of the mesh - I hope it makes clear what I want to achieve.

I found the “Follow active quad” method and the UV Squares addon (which seems to me is doing just the same as the follow active quad function) but then I get the following result: (3 in the image)

This happens all the time and as far as I understand / see these weird misplacements happen on faces which are no quads. The mesh is not crazy difficult so I think I might just do a little remeshing, adding/removing some edges here and then to make all faces quads but at this point I just want to be sure: is that actually the way to go? All tutorials I find about this topic always work with just quad meshes but at least when I model all the time the resulting topology becomes a little bit messed up in the sense that it is not quad-only (for example when beveling or using booleans). Addionally the least models I find out there are quad-only so I really wonder: how is it possible to create good (in this case: straighten) UV maps when the mesh is not quad-only? OR is there some secret trick to achieve the straighten UV map though?

There are different ways to do it but the best way i found is to use the free UV Squares addon. However, this addon won’t work properly for non-quads, so you’ll probably have to pin down the quad vertices and then unwrap the non-quads.

hmmm… as described I already use the UV Squares addon but it brings the same results. What do you mean with “pin down” the quad vertices?

You can pin down the vertices in the UV editor by selecting them to active and pressing P. Pinned vertices turn red. Then when you unwrap it again the vertices that aren’t pinned down will follow the corresponding pinned vertices.

That being said, I would recommend you redo the model. The way I would do it is to make the basic shape by extruding the cube and using 2 bevel layers for the edges. You can use the modifier or ctrl B it doesn’t matter. That will keep everything a quad and unwrapping will be much easier.

okay, thank you for your feedback!

You may try the rectify option from :

no, another addon does not solve the problem

Well… your model does also seems to have some triangles… but it seems to be “rectangable” … so you might just “play” with the options or share the model… ??