Is the paternity system feminist?

It's not biased against men, it's centered on the best interest of children. This can often cause perceived injustice for both men and women.

I completely agree that paternity testing should be routine and on an opt-out rather than opt-in basis. However, many men will still end up on the hook for non-bio children if they opt to stick around knowing the child isn't theirs. At least it will be an informed choice though.