At least in theory, it may be possible for people to find common objectives even when their values are fundamentally different. For instance, some conservatives support raising the minimum wage on the ground that it reduces the number of low-skill jobs and deters illegal immigration.

If you really want a topic where people with very different values and world views agree, look at the attitude towards Greece defaulting. There you can find people arguing that a Greek default would be good because it will lead to X which is good according to my values, and others arguing that a Greek default would be good because it will lead to not X which is good according to my values.