Guns are definitely an issue for a lot of characters in the mild powers tier (re: using the definition I posted previously, for specific reference purposes). However, it depends on where in the tier the character is, too. A character at the upper end of the tier can probably deal with them. Once you hit sort of that point where a character can conceivably cross over from one tier to the next, guns become very much standard "tools of the trade" in that they're useful, but not game-changing. At that point, they're no longer much of an issue at all.
My main character is definitively "mild powers." He's square in the middle of the tier. He has ablative armor designed to withstand gun-shots and slashing attacks, but someone with a .357 Saturday Night Special will end the fight post-haste if they put six in his chest if for no other reason than that they've done so much deep tissue trauma to him that he's going to be hard-pressed to keep fighting. That's assuming his armor holds up after the first two or three shots - if not, he's very likely dead If the opponent is, say, 30 feet away, well -- there's not much hucking or jiving he can do to get out of the way. In the words of the helicopter machine gunner from Full Metal Jacket, you just don't lead 'em as much.
On the other hand, my Shadowrun character can eat a faceful of birdshot and not give a shit. He's at the upper end of the mild powers spectrum or the bottom of the next one depending on how you choose to classify him. He's basically a punch wizard with enormous amounts of damage soak. To him, a gun is a potential danger, but it's something he can fight against. Someone with armor piercing shells could do some damage to him, but something like a .22 is going to bounce off of his skin because he's a (literal) troll.
A lot of characters at mild powers, barring specific power sets or gear, aren't equipped to deal with the speed, range, or potential tissue damage of a gun-shot. You can circumvent a lot of the issues that come with modern firearms by utilizing magitech or future-tech weapons that are specifically designed for that purpose. I've seen a lot of people play "gun-mages" who do exactly that.