That is what I have ended up doing. Except when the artwork is licensed under a LGPL, GPL, CC, etc. license that grants anyone the rights to share and remix. The only thing that is kind of iffy is the attribution part:
"– You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work)."
Many distributions have their artwork released under this license, and should for most of the part be OK to use. Nevertheless, as long as you do not use any artwork with any negative intentions, most of these distributions would probably want their community to do these kind of things.
This goes for Manjaro, Sabayon, Gentoo, and several others.
Not that would want to make a t-shirt with every distributions that is out there (Arch and Debian is two distributions I highly respect, and some other artwork is somewhat known and looks nice), but it made me curious to see what kind of policies the distributions have for use of their trademarks. As I would believe that creators would want their community to spread walk around with commercial for free to spread their work, it seems to be harder than it should be for some instances, but that most distributions have strict guidelines is understandable.
However, community creativity and openness seems to not always follow the open source ideology of GNU/Linux, as I would expect in a higher degree than what it seems. Often, remixes as long as it resembles the original logo, and colors to match color of the t-shirt (or if you prefer colors of your own likings), and in no disrespectful manner could but a personal feel to the products, and I can not see how this can harm a distribution. Although I can see how it can feel daunting to give this much freedom to use trademarks for many purposes.
Some of them have very useful information on what you are allowed to do and not. Considering if you are allowed to use for these intentions. For example, the:
Arch Linux says that logo for personal usage is perfectly fine, and that it is covered under Fair Use . Their trademark say this however (as I read today):
"Restricted use that requires a trademark license
Use for merchandising purposes, e.g. on t-shirts and the like."
Commercial use is already covered in the list, if this was regarding use, it should already be covered, so I would interpret that as a general rule for both non-commercial and commercial use. I am not from an English speaking country, so might not have the correct understanding of the word, but this is Google's definition:
"the activity of promoting the sale of goods, esp. by their presentation in retail outlets."
In this case it would not be promoting sales of Arch Linux, since it is free.
Debian have information about use of their logo on these two pages:
"Debian logos and marks may now be used freely for both non-commercial and commercial purposes."
"You can make t-shirts, desktop wallpapers, caps, or other merchandise with Debian trademarks for non-commercial usage."
However, it is released under English under a LGPLv3 or later, or if you want, CC BY-SA 3.0, and a stylized word “debian”, which is apparently not copyrightable. Meaning that it should be OK to use this logo also with slightly altering the image, at least for personal use.
The OpenSuse logo have very specific rules on colors, placement of logo and text, font, etc. But their Geeko logo can have its own colors, and be altered.
They also give this information:
You are welcome to make use of the openSUSE Marks to produce merchandise such as t-shirts, hats, bags, jackets, sweatshirts, mugs, and desktop wallpapers and give them to your friends, family, community members, provided there is no commercial interest behind it. You have to request permission if you want to commercially distribute articles using the openSUSE Marks (see "Contact Information" below to request permission).
As well as:
Fedora requires permission:
Usage That Requires Permission
"Community members may request from the Fedora Board a license to use the Fedora trademarks on non-software related goods, services, or other entities. The Board, or someone it delegates for the task, will ask to see the proposed designs before approving the use."
Ubuntu also seems to have strict rules regarding colors and alignment:
And I would also need a written agreement for use of their logo in this manner.