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
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf
A seamless background texture of old cardboard.
Source V. Hartikainen
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
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
This one needs to be used in small areas; you can see it repeat.
Source Luca
Lovely light gray floral motif with some subtle shades.
Source GraphicsWall
Simple wide squares with a small indent. Fits all.
Source Petr Šulc.
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Remixed from a design on Pixabay. To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
Prismatic Polyskelion Pattern No Background
Source GDJ
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Smooth Polaroid pattern with a light blue tint.
Source Daniel Beaton
From an image on opengameart.org shared by rubberduck.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
A seamless pattern created from a square tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
An emulated “transparent” background pattern, like that of all kinds of computer graphics software.
Source AdamStanislav
Prismatic Abstract Line Art Pattern Background
Source GDJ