meaning - "wouldn't agree" vs "don't agree"

Could I say

"I wouldn't agree with you"

instead of saying

"I don't agree with you"?

If I could, in which situation should I use the construction "I wouldn't agree with you"?

I'm wondering if the "I wouldn't agree with you" version is more polite than 'I don't agree with you'.

Moreover, I often come across that people use it without an "if clause" or an "if clause" is removed. Why?