Wow this is a tricky one!
To help, let's consider another instance where we might see this construction
I would rather clean the garage myself than ask that John clean it.
The subject is stating that he would rather go through the trouble of cleaning a room than ask John (maybe John is annoying).
I would rather clean the garage myself than to ask that John clean it and be disappointed.
The subject is stating that he would rather go through the trouble of cleaning a room than ask John because John would not clean it well and that would disappoint the speaker
I would rather clean the garage myself than ask that John clean it and be disappointed.
Interestingly, this reads like a run-on in that who is disappointed is ambiguous. Obviously, we can semantically infer that it is the same as the last sentence, i.e., it is the speaker that would be disappointed. However, it is a grammatically correct interpretation to read this as the speaker asking John to both clean the room and be disappointed (semantically, asking someone to be disappointed is preposterous).
We return to the example text:
I would rather take a political risk in pursuit of peace, than to risk peace in pursuit of politics.
The use of the infinitive here could be to clearly mark this clause as a distinct verb phrase (further emphasized by the comma [pause]). The parallelism is maintained on a verb phrase level with "take a political risk..."
...I feel like I may be overlooking something simple though, so I look forward to the discussion and resolution of this query!!