Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
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
I have no idea how to describe this one, but it’s light and delicate.
Source JBasoo
This pattern comes in orange, and it looks as if it is "made of glass".
Source V. Hartikainen
A nice and simple gray stucco material. Great on its own, or as a base for a new pattern.
Source Bartosz Kaszubowski
A repeating background with dark brown stone-like texture and abstract pattern that looks like tree trunks.
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
You just can’t get enough of the fabric patterns, so here is one more for your collection.
Source Krisp Designs
Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
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
Prismatic Geometric Pattern Background
Source GDJ
Not so subtle. These tileable wood patterns are very useful.
Source Elemis
One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
From a drawing in 'Gately's World's Progress', Charles Beale, 1886.
Source Firkin
Snap! It’s a pattern, and it’s not grayscale! Of course you can always change the color in Photoshop.
Source Atle Mo
Formed from a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Classy golf-pants pattern, or crossed stripes if you will.
Source Will Monson
A seamless pattern created from a square tile. To get the tile, select the pattern in Inkscape and use shift+alt+i.
Source Firkin
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
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A pattern drawn in Paint.net and vectorized in Inkscape.
Source Firkin