Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
Light square grid pattern, great for a “DIY projects” sort of website, maybe?
Source Rafael Almeida
Super subtle indeed, a medium gray pattern with tiny dots in a grid.
Source Designova
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
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
Remixed from an image that was uploaded to Pixabay by Pixeline
Source Firkin
Vertical lines with a bumpy, yet crisp, feel to it.
Source Raasa
A car pattern?! Can it be subtle? I say yes!
Source Radosław Rzepecki
A browner version of the original weathered fence texture.
Source Firkin
A repeating graphic with ancient pattern. I came up with this name/title at last minute, so you may find that there is very little of ancientness in this pattern after all.
Source V. Hartikainen
A slightly more textured pattern, medium gray. A bit like a potato sack?
Source Bilal Ketab
You don’t see many mid-tone patterns here, but this one is nice.
Source Joel Klein
A seamless pattern created from a square tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
All good things come in threes, so I give you the third in my little concrete wall series.
Source Atle Mo
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868.
Source Firkin
The image depicts an edo-era pattern called "same-komon" or "鮫小紋"which looks like a shark skin.The "same" in Japanese means shark in English.
Source Yamachem
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
Zero CC bark from fur tree tileable texture, photographed and made by me. CC0
Source Sojan Janso
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
Subtle scratches on a light gray background.
Source Andrey Ovcharov
Inspired by a 1930s wallpaper pattern I saw on TV.
Source Firkin
Derived from an image that was uploaded to Pixabay by Kaz
Source Firkin