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
Abstract Tiled Background Extended 12
Source GDJ
This one is rather fun and playful. The 2X could be used at 1X too!
Source Welsley
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
One more in the line of patterns inspired by Japanese/Asian styles. Smooth.
Source Kim Ruddock
White fabric looking texture with some nice random wave features.
Source Hendrik Lammers
Prismatic Geometric Pattern Background 2
Source GDJ
Here's a bluish gray striped background pattern for use on web sites.
Source V. Hartikainen
Actually remixed from a pattern on Pixabay. But then noticed a very similar one on Openclipart.org uploaded by btj51q2.
Source Firkin
Derived from an image that was uploaded to Pixabay by Darkmoon1968
Source Firkin
This one could be the shirt of a golf player. Angled lines in different thicknesses.
Source Olivier Pineda
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
A seamless pattern formed from cross 4. To get the original tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
The classic 45-degree diagonal line pattern, done right.
Source Jorick van Hees
Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).
Source GDJ
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Here's a new background image for websites with a seamless pink texture. It should look beautiful with website themes where light pink background is needed. The background is seamless, therefore it should be used as a tiled background.
Source V. Hartikainen
Seamless Olive Green Web Background Image
Source V. Hartikainen
A free background image with a seamless texture of cardboard. This texture of cardboard looks quite realistic, especially when is actually tiled.
Source V. Hartikainen
Just a nice looking textured pattern with faded blue stripes. Well, that's it for today... one background a day, as usual.
Source V. Hartikainen
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin