Can I make this cake WITHOUT the cream cheese? I don't like cheese. Please respond right away, because I want to make this very soon! Thanks!

Following drbabs and aargersi on taste.
But if you don't want to use cream cheese at all, soft or silken tofu may work as a replacement.

I agree with Dr Babs, I’ve had this cake several times and it doesn’t taste of cheese at all, it’s just creamy coconutty goodness.

The cream cheese here is a vehicle for the coconut filling. Since you’ve never made it before, my suggestion would be to use the cream cheese anyway. Once you mix it with egg, vanilla, sugar and coconut, it’s unlikely that you will taste the cream cheese.