The following two pictures are displaying the same place using a slightly changed view direction.

It has been tested using grid-1.16.2-fabric0.17.2-1.6.jar on a relevant game instance and loader on all the graphic modes (from fast to fabulous) and the Java runtime is v1.8.0_251

Whereas the grid blocks are rendered as requested in the first screenshot above (a 5x5 grid of blue squares), as soon as you are looking downward, the rendering is unexpectedly drawn in white with interfering lines as you may see in the second screenshot.

Disable Fabritone and Grid will work as it should.

Please tell me how could I do that?
My other mods are:
[✔️] beenfo-1.16.2-fabric0.17.2-1.1.1
[✔️] blockmeter-1.16.2-fabric0.17.2-1.5.1
[✔️] collective-1.16.2-1.38
[✔️] easyelytrato_1.16.2-1.5
[✔️] fabric-api-0.18.0+build.397-1.16
[✔️] fabricmod_VoxelMap-1.10.10_for_1.16.2
[✔️] grid-1.16.2-fabric0.17.2-1.6
[✔️] modmenu-1.14.6+build.31
[✔️] orderly-2.0.0-alpha.10-1.16
[✔️] shulkerboxtooltip-2.1.1+1.16.2
[✔️] Unsuspicious-Stew-0.1-Fabric-1.16.2
[✔️] worldtime-1.16.2-fabric0.17.2-1.2.4

Exactly.

For the record, I looked for an alternative map+waypoint handler, and found that Xaeros stuff (mini+world map) seemed to work without issue with Grid.

This is strange, because I'm trying with VoxelMap right now, and don't seem to have any problem. This is with some other mods you don't have, and you have some mods that I don't have, so I'm trying to recreate a MC instance that has exactly the same setup as yours. Can you post a complete log file (with Voxelmap, that has the problem) to pastebin or something and link it here?

Here's 1 day expiry pastebin of a buggy execution trace: https://pastebin.com/6sZJkCjY

Thanks for the paste. I'm sorry, but I'm giving up on this for now; I recreated the exact mod list you're using (including beem and Autofish for example), and the bug just doesn't happen to me.

On a side node, as I see you're using several of my mods, and you seem to be speaking French from your paste, I'd be happy if someone helped me with french translations of my mods at https://crowdin.com/profile/gbl :)

Oh. Seems I answered too quickly. There is a mod called Fabritone that causes the excact display problems that you're describing, so I thought you had that. Seems to be another mod in that list.

Does that easyelytrato even work for you? It seems to a Forge mod to me (and also collective, which is just a library for easyelytrato).

I found easylytrato useful few months ago as I wasn't skilled at elytra on a previous version, but it seems that I can manage without it now, so 2 mods to remove (good!).
Trying different mod activation/configuration, I found that VoxelMap was the offending one.

Oh wait. So this problem does happen with VoxelMap and doesn't happen without it? Thanks, that'll hopefully help me find the problem.

Unchecked mods are disabled (not loaded). VoxelMap has cached data and stored waypoints on the displayed area.

I gave translations to most of your mods I used (even if now some of them aren't relevant).

Here's an example of what it looks like for me - two BlockMeter boxes, a Beem beam, two VoxelMap beacons, and Grid blocks. Sorry, I just can't reproduce your bug.

Thank you for the translations, they'll be in my next mod versions!

This is with:

Mods:
  [✔️] Autofish-0.9.0-fabric-mc1.16.2
  [✔️] beem-1.3.2
  [✔️] beenfo-1.16.2-fabric0.17.2-1.1.1
  [✔️] blockmeter-1.16.2-fabric0.17.2-1.5.1
  [✔️] fabric-api-0.18.0+build.397-1.16
  [✔️] fabricmod_VoxelMap-1.10.10_for_1.16.2
  [✔️] grid-1.16.2-fabric0.17.2-1.6
  [✔️] modmenu-1.14.6+build.31
  [✔️] orderly-2.0.0-alpha.10-1.16
  [✔️] shulkerboxtooltip-2.1.1+1.16.2
  [✔️] Unsuspicious-Stew-0.1-Fabric-1.16.2
  [❌] worldtime-1.16.2-fabric0.17.2-1.2.4.jar (disabled)

Have you tried rendering the VoxelMap waypoints in beacon-only mode?
This is my usual configuration, and hence, the one which trigger the drawing bug!

Wow, that does it!
Sings, both, and off don't cause the problem, but beacons-only does. Now at least I can test it.

Nice! And incidentally, this should also work with Fabritone!

Found it and fixed it! VoxelMap, in waypoints-are-beacons mode, changes a GL setting, which it does reset when drawing signs, but leaves changed otherwise. Now I explicitly change that setting back before drawing Grid. Just uploaded new versions for 1.16.1 and 1.16.2, which already contain your french translations!