If you really have to mention something, don't complain.
"hey boss, who controls the reading material provided in the break
room?"
If he asks why simply say:
"I thought maybe I could request something I find really interesting.
It has great topics that are safe for a work environment and could
also help people relax with a rough day".
This is not confrontational, and provides you the information you need while subtly acknowledging there is something maybe not work appropriate that is being provided.
Once you talk to who ever choses, provide your suggestion!
Hey, I really want to read TMZ! They are a tabloid that covers many
interesting topics, but have a very high fact check rating where they
are even being sourced by large media outlets. would it be possible to put in a request for this? I know a few other employees would enjoy them too! I was also curious, I noticed that this month, we started getting issues of DM. I know they don't have the best of reputations and was wondering why we would take the risk of possibly upsetting a client if they saw it laying around?
Ultimately though, it's just something you need to deal with. At my job, they provide TV's along the walls of the break room on one of our floors. These channels cannot be changed and usually have news on. The channels they usually have on are ones I do not agree with as every time I walk by, there is a blatant lie for a headline posted and being discussed.
I don't complain about it, nor do I make it a big deal. People can put on whatever they want. I have made the choice to instead eat at my desk or eat in a different break room. While the news may not be a hate-filled source compared to what you are talking about, it's not something worth making a fuss over. I am 1 employee of hundreds here with a constant flow of new recruits every day. The risk is not worth finding a new job for.
Many companies secretly or publicly take political stances. For example, Chika-fil-a is a well known conservative company. By the same token, Starbucks is fairly progressive in their stances. My company sent out an email to everyone during election time to ask people to vote a certain way with local bills. They didn't take a political stance, but rather explained how it would affect our company if it passes or not and then asked people to vote for it in the way that benefits the company. Of course, people are still entitled to do their own thing but every company has a different way of going about politics.
It is possible that you are working for a company that shares different political values than you and the majority of the employees may actually enjoy the DM (despite whatever blatant crud is thrown in there). It is important to look up the company as a whole before accepting a job, to view everything they represent. Politics, activism, community service, global impact (if it is that large), and decide if those practices and beliefs match your own.
Maybe this was picked by 1 person who thought they could pick whatever they want since they are on the committee and wanted to annoy people, maybe it was picked by the brass, maybe it was picked based on the political views of the company/employees as a whole. If at the end of all this, you realize that the company is not right for you, then it is a learning experience to proceed next time in finding out everything you can about them before accepting.