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 square grid pattern, great for a “DIY projects” sort of website, maybe?
Source Rafael Almeida
Based on several public domain drawings on Wikimedia Commons. This was formed from a rectangular tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Prismatic Abstract Background Design No Black
Source GDJ
This is the remix of an Openclipart clipart called "Maze" uploaded by "any_ono_mous".Thanks.This is a seamless pattern of a maze.
Source Yamachem
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
Derived from an image that was uploaded to Pixabay by Darkmoon1968
Source Firkin
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
By popular request, an outline version of the pentagon pattern.
Source Atle Mo
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
This is so subtle: We’re talking 1% opacity. Get your squint on!
Source Atle Mo
No, not the band but the pattern. Simple squares in gray tones, of course.
Source Atle Mo
Background Wall, Art Abstract, Star Well & CC0 texture.
Source Ractapopulous
A seamless pattern the starting point for which was a 'colour modulo' texture in Paint.net.
Source Firkin
Prismatic Curved Diamond Pattern 3 No Background
Source GDJ
Remixed from a design on Pixabay. To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
A large pattern with funky shapes and form. An original. Sort of origami-ish.
Source Luuk van Baars
Smooth Polaroid pattern with a light blue tint.
Source Daniel Beaton
You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
A repeating background of beige (or is it more vanilla yellow) textured stripes. One more background with stripes.
Source V. Hartikainen