It depends on who we are. I, personally, very much enjoy and appreciate difference in preferences (such as "I like pink, and you like blue," or "I like dance performances, and you like camping.") Preferences/lifestyle are the things that make people different, and I really do enjoy and appreciate that kind of difference.
With opinions, though, I can respect that someone else has a right to his opinion; but I don't think we expect more of ourselves than that. If my opinion is that my kids are better off if I work part-time, and yours is that kids are better off if I don't work at all... All I can respect is that you have a right to your opinion, and I have no right to have an opinion about what you do with your kids and job. In a case like this, I'm most likely willing to consider that I could be wrong; but without evidence that either you or I are absolutely wrong about our own situation, that's as far as I'll go.
Sometimes, though, one person has a more knowledgeable/educated opinion than someone else. If I know my own child and think, say, seeing a certain movie would be disturbing for him; and you don't know my child and think I'm wrong about not letting him see the movie - then my opinion is based on more information/knowledge about my child than your is - so I see no reason (in a situation like this) that someone should "appreciate" the less educated/informed opinion.
We can respect other people as equals (a lot of people don't), and we can realize that they are capable and know themselves, their own families, their own lives, and own situations better than we do. We can respect the opinions about one field or another by someone who has studied extensively in that field; but we don't have to respect that person's opinion about whether we should buy that new house or not.
So, the point is, I think all people always deserve equal respect (and particularly to be viewed as capable of knowing what is right for them and their families). Not all opinions are equal, though, so I can't see how expecting to view them all as "equal" is at all realistic, or even correct/wise.
My "favorite" (sarcasm) thing is when I make a statement that's based on sound knowledge/study, and someone else pulls something out of the blue, presents it, and seems to think our "opinions" are equal. Some people won't offer an "opinion" (other than preference-related) unless they know it's based on sound fact and reasoning. Others think pulling wild ideas out of the blue makes for an equal opinion. They aren't equal, and people shouldn't pretend they are.