Cardioid polar patterns are typically best for recording single voices as they offer the most noise rejection. Bi-polar, or bi-directional, pickup patterns are great for recording interviews as they capture sound from the front and back of the microphone. Omnidirectional pickup patterns capture sound from all directions, which is great for recording a large group of people, but it often captures a lot of ambient noise.
These ideas all might ring true in other area of life, but they don’t have to apply to your singing voice. Singing does not necessarily have to render you “open” and vulnerable to the listener. Try to disconnect from these notions. The best way to do so is to see your voice is an instrument, and your singing is a product of your creativity and skill. Your singing is not a reflection of your “soul” (so to speak).