Kyrgyzstan is generally a safe, welcoming country for travelers, and the areas most visitors spend time in — Bishkek, Karakol, Issyk-Kul — see steady tourism without the kind of incidents that make headlines.
The real safety considerations here are practical, not personal-security ones: altitude on high treks, road conditions on rougher mountain tracks, and weather that can shift fast in the Tien Shan. That's exactly why routes like Altyn Arashan or Ala-Kul are run with experienced local drivers and guides rather than left to a rental car and a map.
Normal travel precautions apply as they would anywhere — keep an eye on belongings in bazaars, use registered transport, and check current government travel advisories for your own country before you go, since those get updated more often than a single blog post ever will.
Zoomy