If you're cut from the same cloth as your cousin, the two of you probably like the same things and think and act similarly. And if two people easily become friends, it's likely because they're cut from the same cloth.
The expression cut from the same cloth likely comes from a period when most people had their clothes made by tailors. Two people might've had their jackets made at different times by the same tailor, but the jackets looked very similar because the same piece of fabric had been used for both. Now the phrase is used more figuratively to say that people share similar qualities, beliefs, backgrounds, or ways of doing things.