1. Like most Chareidim, historically, Shas was pro-peace. The reason Chareidim tend to be pro-peace is that the continued existence of a constant state of war tends to undermine Torah life whether by glorifying soldiers (rather than the traditional Jewish glorifying of Torah scholars), conscription of young adults, and severe economic discrimination against those who haven’t served in the army.
2. Also note that the left wing parties and Chareidim usually agreed on social programs that benefit the poor, whereas the more nationalist parties tend to be less than thrilled about creating and expanding entitlements.
3. If the left wing parties were no so committed to the anti-religious commandments of their Marxist pseudo-religion, the Chareidim would probably be considered inherently left wing , however the Israeli left regardless of what it feels about issues such as national security and economics, sees its highest priority as being to opposed Torah and the Chareidim (to make Israel into an “Am Hofshi” – free from Torah).