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
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857
Source Firkin
Drawn in Paint.net using the kaleidoscope plug-in and vectorised.
Source Firkin
Prismatic Abstract Geometric Background 5 No Black
Source GDJ
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
You guessed it – looks a bit like cloth.
Source Peax Webdesign
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape 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 black tile-able background with paper-like texture.
Source V. Hartikainen
Beautiful dark noise pattern with some dust and grunge.
Source Vincent Klaiber
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
Classy golf-pants pattern, or crossed stripes if you will.
Source Will Monson
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
I’m not going to lie – if you submit something with the words Norwegian and Rose in it, it’s likely I’ll publish it.
Source Fredrik Scheide
Could remind you a bit of those squares in Super Mario Bros, yeh?
Source Jeff Wall
Bit of a strange name on this one, but still nice. Tiny gray square things.
Source Carlos Valdez
Abstract Ellipses Background Grayscale
Source GDJ
From a drawing in 'Uit de geschiedenis der Heilige Stede te Amsterdam', Yohannes Sterck, 1898.
Source Firkin
Light and tiny, just the way you like it.
Source Rohit Arun Rao
A seamless light gray paper texture with horizontal double lines.
Source V. Hartikainen
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
Remixed from a drawing in 'Prehistoric Man: researches into the origin of civilisation in the old and the new world', Daniel Wilson, 1876.
Source Firkin
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective