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 seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
Seamless pattern formed from a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
This one is super crisp at 2X. Lined paper with some dust and scratches.
Source HQvectors
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
Prismatic Groovy Concentric Background 2
Source GDJ
Remixed from a drawing in 'The Canadian horticulturist', 1892
Source Firkin
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
A seamless pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
A seamless pattern the starting point for which was a 'rainbow twist' texture in Paint.net.
Source Firkin
A bit like smudged paint or some sort of steel, here is scribble light.
Source Tegan Male
Zero CC tileable Crackled Cement (streaks) texture, photographed and made by me. CC0
Source Sojan Janso
Here's a quite bright pink background pattern for use on websites. It doesn't look like a real fur, but it definitely resembles one.
Source V. Hartikainen
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
This background has abstract texture with some similarities to wood.
Source V. Hartikainen
8 by 8 pixels, and just what the title says.
Source pixilated
Horizontal and vertical lines on a light gray background.
Source Adam Anlauf