I cannot accept an alternate view on almost any issue--if I could, then it wouldn't be an alternate view, it would be MY view.
I can accept that there are some issues in which there is legitimate room for a difference of opinion, but I think we all feel that we have arrived at the best opinion for ourselves in those issues too. If we didn't, we'd be changing our opinions.
And then there are some issues for which alternate views are simply incorrect--like that the Earth is (roughly) spherical--where I can't even allow for the possibility that someone else could legitimately come to a different conclusion.
EDIT: Upon reflection, I suppose I should say that the only alternate views that I could even possibly accept are those which I have not yet heard or considered--because I'm always open to new evidence. But for those views and opinions which I have already considered and rejected for one reason or another, I'm not really open to accepting them.