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
A gray background pattern with a texture of textile. Suits perfectly for web design.
Source V. Hartikainen
So tiny, just 7 by 7 pixels – but still so sexy. Ah yes.
Source Dmitriy Prodchenko
This is a grid, only it’s noisy. You know. Reminds you of those printed grids you draw on.
Source Vectorpile
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Nothing like a clean set of bed sheets, huh?
Source Badhon Ebrahim
I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
Prismatic Geometric Pattern Background No Black
Source GDJ
A background pattern inspired by designs seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
This is a grid, only it’s noisy. You know. Reminds you of those printed grids you draw on.
Source Vectorpile
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Snap! It’s a pattern, and it’s not grayscale! Of course you can always change the color in Photoshop.
Source Atle Mo
From a drawing in 'From Snowdon to the Sea. Striking stories of North and South Wales', Marie Trevelyan, 1895.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin