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
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
This is a remix of "flower seamless pattern".I rotated the original image by 90 degrees.This is a seamless pattern of flowers.These horizontal wavy lines are one of Edo patterns which is called "tatewaku or tachiwaku or 立湧" that represents uprising steam or vapor.
Source Yamachem
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
A seamless stone-like background for blogs or any other type of websites.
Source V. Hartikainen
Simple wide squares with a small indent. Fits all.
Source Petr Šulc.
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
The name Paisley reminds me of an old British servant. That’s just me.
Source Swetha
A pattern formed from repeated instances of corner decoration 8. To get the basic tile select the rectangle in Inkscape and use shift+alt+i
Source Firkin
From a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
Zero CC tileable ground (#2) cracked, crackled texture, made by me. CC0
Source Sojan Janso
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
A background pattern with green vertical stripes. A new striped background pattern. This time a green one.
Source V. Hartikainen
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Colorful Floral Background 3 No Black
Source GDJ
Don’t look at this one too long if you’re high on something.
Source Luuk van Baars
Snap! It’s a pattern, and it’s not grayscale! Of course you can always change the color in Photoshop.
Source Atle Mo
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić