If hiking makes you feel anxious, then don't go hiking.
If you do go hiking, as with most activities, you should pay attention to what your are doing. That includes listening to what is around you. Part of the enjoyment for most hikers is experiencing the outdoors. You can't do that as fully when you disable one of your senses. Leave the music player and headphones home, and instead listen to the birds, the insects, the water running nearby, the sound of your feet on different surfaces, or that unexpected rustle off to the side. If these are really not as interesting, fun, soothing, and stimulating to you as music, then I don't understand why you go hiking in the first place.
There is also a safety issue. To be fair, the things I'm about to describe are unlikely occurances, so most of the time you can be oblivious to them and get away with it. However, these things do occasionally happen, so having your ears open can be the difference between having a hike and being a statistic. For example, hearing a hissing sound 10 feet in front of you by the side of the trail can prevent a rattlesnake bite. Hearing little rattling sounds or even rumbling on the slope above you can alert you to falling rocks. Unstable snow sometimes makes a sound, which can warn of avalanche risk. A swooshing sound can help you prepare to not get sand blown in your eyes from a dust devil. Bears sometimes make huffing sounds as a last warning. A gurgling sound under the ice signals obvious danger, as does a cracking sound. Keeping track of the direction of gunshot sounds is a really good idea. Hearing the whistling of a bullet means you almost got hit, and it's time to do something about it.
If you think that last one is far fetched, it has actually happened to me. I got down on the ground and yelled as loud as I could. The yahoos around the hill a bit packed up their rifles and beer coolers and skedaddled out of there. They may have thought they hit me, and didn't want to be identified. At least it was a peaceful night after that.