Please consider adding an option in the mod's config that let's you disable particle effects from yourself if you are in first-person. Some hats, while having cool designs, are too distracting to use. I don't want to be avoiding cool hats just because they happen to be annoying to use.

If you are using a mod that adds first person model rendering (Which is what causes hats and particles to render in first person) set forceFirstPersonNoRender to true in the config

Now that's odd: I double checked in my WIP 1.21.1 private modpack if I had particles in first-person or not, and apparently I don't despite this being a problem in older versions of the pack (though some mods aren't updated yet, so that may change). I'll just keep your tip in mind.

On the other hands, I noticed that if I opened my inventory, the particles starts rendering until I close it, but only if it's an inventory where I can see my character. Apparently the preview model in your inventory counts as being in third-person.

Yeah the way Minecraft handles the inventory screen is re-rendering your actual player model as though its third person, instead of like a fake version of the player, which will cause third person effects like the particles to start rendering.