Got some felt in my mailbox today, so I scanned it for you to use.
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
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i
Source Firkin
More in the paper realm, this time with fibers.
Source Jorge Fuentes
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
A repeating background of thick textured paper. Actually, it turned out to look like something between a paper and fabric.
Source V. Hartikainen
Simple wide squares with a small indent. Fits all.
Source Petr Šulc.
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
A version without colours blended together to give a different look.
Source Firkin
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892. The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
A free tileable background colored in off-white (antique white) color.
Source V. Hartikainen
Remixed from an image that was uploaded to Pixabay by Pixeline
Source Firkin
And some more testing, this time with Seamless Studio. It’s Robots FFS!
Source Seamless Studio
A seamless pattern the starting point for which was a 'light rays' rendering in Paint.net.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Prose and Verse ', William Linton, 1836.
Source Firkin
Smooth Polaroid pattern with a light blue tint.
Source Daniel Beaton
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
From a drawing in 'A Life Interest', Mrs Alexander, 1888.
Source Firkin
To get the tile this is made up from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Abstract Line Art Pattern Background 2
Source GDJ
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin