I don't. I hear about stuff anyway, mainly discussion of issues on social media, but without a rolling backdrop of horror images and the doom tones that TV news reports (and some of the sensationalist online news media) generally have. I will go and look up coverage or discussion if I want to find out about something, and subscribe to a couple of current events podcasts, but don't listen to every episode.
What do you do with this social responsibility? I'm not being snarky, I'm genuinely curious as to how it's helpful. I don't see that making myself anxious or upset about things happening millions of miles away that I have no control over helps anybody. To me, social responsibility is about having a positive effect with my direct actions where possible; trying to raise my children to be good people, avoiding creating too much waste, contributing to things where I can make a difference (e.g. donating time/money), being kind in everyday interactions, doing the best that I can at work, putting positivity/hope/understanding/curiosity out into the world.
There is research which shows that when we read/hear/see events that would provoke a defensive or danger response IRL it provokes some level of that response in your body anyway, even though the danger is not actually applicable to you directly. The thing is that this response isn't completely benign, when it's balanced it is, because it's meant to provoke action. It diverts resources from other areas of your body in order to enable that action, because the occasions where you do experience physical danger IRL are much rarer so it doesn't matter because you can spare a bit of thinking power, empathy, calm, seeing the bigger picture etc when you need to address an urgent threat. But you don't want to be drained of those things at the rate that we hear about disasters and atrocities in the news, that's not helpful to your everyday functioning. And it's not healthy to keep having an urgent threat response and then not using that capacity for action against the threat.
People will have different tolerances of course, so some people can watch the news every day and find that this is fine and they are happy with their level of action and don't feel unduly stressed and anxious, but if anyone is struggling with anxiety, cutting down on exposure to rolling news is a good idea to try, and I don't see that it is irresponsible to do that if it helps protect someone's ability to do other things which are good in the world.