Sure you can. Weapons research is a very common counterexample; people have been solving political problems with technical solutions ranging from sharpening spear-heads to achieving nuclear chain reactions.
(Of course "who is politically right" and "who has the most technical expertise on their side" are at best tenuously related, but that's a different and longstanding problem. If you believe you're politically right and you have technical expertise on your side, use it.)
Encryption also solves the political problem of "I need to communicate plans with my allies across long communications links without my enemies knowing what they are," which can often be opposed to violence (notify people of an opposing military action, evacuate armies or civilians, coordinate a plan to surrender without showing weakness, coordinate a plan to demand the other side surrender by showing so much strength they won't fight, etc.). Much early encryption research was for governments who were already targets to hide data from other governments.
Electronic voting machines. Digital signatures on passports. Long-distance communication, whether by telegraph, radio, or satellite. Norman Borlaug's wheat hack. Machine translation. The counting machines that powered the Holocaust (as mentioned, something being a political problem solvable by technical means does not mean it should be solved). Forensic analysis of DNA and fingerprints. Eurovision. Irrigation. Aqueducts. The printing press. I feel like there are many things....
(Of course "who is politically right" and "who has the most technical expertise on their side" are at best tenuously related, but that's a different and longstanding problem. If you believe you're politically right and you have technical expertise on your side, use it.)