Hexagonal dark 3D pattern. What more can you ask for?
Source Norbert Levajsics
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
Subtle scratches on a light gray background.
Source Andrey Ovcharov
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
More tactile goodness. This time in the form of some rough cloth.
Source Bartosz Kaszubowski
This metal background pattern resembles a metal plate with rivets. Solid rivets on a metal plate.
Source V. Hartikainen
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
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
ZeroCC tileable mossy (lichen) stone texture, edited from pixabay. CC0
Source Sojan Janso
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury