What relevance do the polarities of pigments found in spinach bear on the spinach's photosynthetic activity?

The first bit has to do with protecting the plant cells when there is bright light. Light is good but when there's a lot of it the amount of glucose the plant cells make can build up in the cell fast, and that can mess up the osmotic balance (glucose concentration too high). The plant cell can store it as insoluble starch until later, and that solves the problem.

The different pigments allow the plant to harvest energy from a broader range of light wavelengths than chlorophyll a alone. This means the plant can make more glucose/starch from the same amount of light.

The polarities of the molecules will determine how they are positioned inside the thylakoid membranes, a non-polar environment. If photosynthesis happens in the membranes, and the pigments are non-polar, it would allow the pigments to be 'where the action is' and the light energy would not be wasted. A polar group stuck onto the molecule would help it to keep 'right side up' in the membrane. These bits can also help keep the membrane from ionizing by acting as antioxidants.

So basically these are all things which allow the plant to make the most of the light energy it gets, with the most efficiency, without damaging itself. More energy will be stored in these plants than in plants that don't have these adaptations.