A free seamless background image with abstract texture of green "curtain".
Source V. Hartikainen
If you like it a bit trippy, this wave pattern might be for you.
Source Ian Soper
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Super subtle indeed, a medium gray pattern with tiny dots in a grid.
Source Designova
Paper pattern with small dust particles and 45-degree strokes.
Source Atle Mo
Alternative colour scheme. 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 an image that was uploaded to Pixabay by Pixeline
Source Firkin
Nicely crafted paper pattern, although a bit on the large side (500x593px).
Source Blaq Annabiosis
Derived from an image that was uploaded to Pixabay by mdmelo.
Source Firkin
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Inspired by a pattern seen on a public domain image of a very old tile. To get the unit cell, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
This is a semi-dark pattern, sort of linen-y.
Source Sagive SEO
Background Wall, Art Abstract, Blue Well & CC0 texture.
Source Ractapopulous
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin