I'd say none, because one does not give their judgements or opinions to an issue, one gives their opinions and judgements to an audience regarding an issue, even if you yourself are the audience. Just think about it logically, you can't give your opinion on a book to the book, or give your opinion on a crime to the crime.
Furthermore, you're using "without first taking a methodical approach" in conjunction with "haphazardly", instead of cancelling "haphazardly" and providing the correct substitute. So essentially what the language says in your example is that it's okay to arrive at a haphazard opinion/view/judgement once you've methodically studied the issue. This of course is self contradictory because you're no longer taking haphazard action after giving serious disciplined and objective effort.
A better way to speak this would be to say:
One cannot haphazardly establish judgement or opinion on such issues,
but rather must methodically study them and draw conclusions as
objectively as possible.