Good question. Chlorophyll is one type of pigment that is part of the machinery of photosynthesis, but there are other pigments that are other colors that can do photosynthesis too.

In fact, even leaves that look green have other pigments in them. You can see these pigments when trees and shrubs lose their leaves in fall (if you live where this happens). The colors of fall leaves were in the leaves all along, but hidden by the chlorophyll.

We see different wavelengths of light as color. Sunlight has all the colors of the spectrum. When light hits an object, some colors are absorbed, others are reflected. When a leaf looks green, all of the other color are being absorbed, but green is bouncing back to your eyes.

Not all wavelengths of light have the same amount of energy. Light at the purple end has more. Light on the red end has less.

If you see an algae that looks red, what colors is it absorbing, and what colors are being reflected to your eyes?

If you are interested in questions like this, you may want to study botany or plant ecology.

All plants that use photosynthesis to make sugars contain chlorophyll. Therefore if a plant does not contain chlorophyll, it will not be able to use photosynthesis. Even though chlorophyll will always be seen as green, there are other pigments that leaves can have that are reddish that cover up the green color. One reason for this is that some plant-eating animals might be attracted to the green color so it helps the plant to cover it up with red. So generally, plants with non-green leaves will have chlorophyll and photosynthesis, unless they happen to be one of the species of parasitic plants that eat other plants for energy.

Sometimes, but mostly not - the chlorophyll pigment is green, and while there are other pigments that also color leaves and are not green, anything that is going to photosynthesize need chlorophyll.