Question

Science ignores

Answer 1

I'd say that science ignores both beliefs and opinions. 
Isaac Newton proposed the universal law of gravitation, science will ignore your opinion and stick to the law. Science doesn't care if you don't believe in gravity. Even if it's your opinion that gravity doesn't exist, science doesn't care because your opinion will not change anything.
I think it's the same with beliefs, if you don't believe in gravity, it won't just disappear. If you don't believe in the color red, the color red isn't going to just disappear... because the real world doesn't care about your opinions and beliefs. 

I hope I made this make sense. 

Answer 2

Neither beliefs or opinions. Science is open to all opinions and beliefs and can use them to make sense. You could use it to connect with your original beliefs.