Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
A very dark spotted twinkle pattern for your twinkle needs.
Source Badhon Ebrahim
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Traced from a drawing in 'Household Stories from the Collection of the Brothers Grimm', Wilhelm Carl Grimm , 1882.
Source Firkin
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Used in small doses, this could be a nice subtle pattern. Used on a large surface, it’s dirty!
Source Paul Reulat
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
Looks like an old wall. I guess that’s it then?
Source Viahorizon
No relation to the band, but damn it’s subtle!
Source Thomas Myrman
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
Inspired by a drawing in 'Kulturgeschichte', Freidrich Hellwald, 1896.
Source Firkin
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
Psychedelic Geometric Background No Black
Source GDJ
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
Super subtle indeed, a medium gray pattern with tiny dots in a grid.
Source Designova
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Here's a subtle marble-like background for use on websites.
Source V. Hartikainen
Looks as if it's spray painted on the wall. You can be sure that this pattern will seamlessly fill your backgrounds on web pages.
Source V. Hartikainen
Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin