Yes. If you want a really good explanation of how it happened and the effects it’s practically the subject of The Premonition by Michael Lewis

The CDC (formally Centers for Disease Control and Prevention) has long tried to enter the gun control debate. That has nothing to do with their mission of communicable disease prevention. Congress has repeatedly voted to block them.

The wider medical community has been vocal about gun control, because guns are a leading cause of injury and death. The fact that it's not a virus or bacteria is arguably a pointless technicality, incidental to saving people's lives. The people who catch the 'bullet' disease are treated at hospitals by doctors.

You may not think it's appropriate, but many doctors disagree. There's nothing in that indicating it's politicized; people may want to politicize gun control, Coronavirus, and lots of other health issues, but that doesn't make the health institutions political for dealing with it. (They also want to politicize the CDC and every other democratic institution (the Post Office, etc.).)

Should CDC also be involved in traffic laws too?

They are not involved in writing traffic laws, but they most certainly are involved in researching traffic caused injuries. It makes sense, because they are a leading cause of death

"Involved in laws" doesn't really describe the CDC exactly, but whatever.

One example of many:

https://www.cdc.gov/sleep/about_sleep/drowsy_driving.html

The CDC is still the Centers for Disease Control and Prevention. It's mission includes but is not limited to infectious disease. Congress has mandated they cover, in addition to infectious disease, research on food borne pathogens, environmental effects on health, occupational safety, injury prevention and how best to promote health. They do research on, for example, obesity and diabetes which are noncommunicable. They also are tasked with education to improve the health of US citizens (or residents, it's unclear). They specifically and explicitly replaced the National Communicable Disease Center, as their mission grew.

Meanwhile, all they've tried to do is research gun violence, not "enter a debate".