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
An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
Prismatic Abstract Geometric Background 2 No Black
Source GDJ
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
An aged paper background tile with smeared and pressed text.
Source V. Hartikainen
Heavily remixed from a drawing in 'Barbara Leybourne; a story of eighty years ago', Sarah Hamer, 1889.
Source Firkin
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Formed by distorting a JPG from PublicDomainPictures
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A hint of orange color, and some crossed and embossed lines.
Source Adam Anlauf
Sort of like the Photoshop transparent background, but better!
Source Alex Parker
Used correctly, this could be nice. Used in a bad way, all hell will break loose.
Source Atle Mo
From a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
Redrawn based on a drawing in 'По Сѣверо-Западу Россіи' Konstantin Sluchevsky, 1897.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Sounds French. Some 3D square diagonals, that’s all you need to know.
Source Graphiste
It’s big, it’s gradient—and it’s square.
Source Brankic1979