When whatever the issue at hand doesn't affect a core value that is disagreed about.
Admittedly, with the extreme polarization we have today such issues are few and far between. The Democrats practically define themselves as being in opposition to whatever the Republicans try to do, even if it's something they themselves were advocating for a couple years ago.
But extending a olive branch isn't particularly hard to do. Just offering to discuss a issue with the other side in a frank but civil way would easily count nowadays.
It's just that both sides, particularly Democrats, are having to deal with the fact that they would rather politically grandstand and bash the other side than actually get anything done, hence the extreme gridlock and animosity we have today.
So the way I see it, the best way to extend olive branches is to constantly offer to try and do actual debates on issues to attempt to knock out some kinda bill to vote on. Now obviously you can't force the other side to be reasonable, but you can't help that. All you can do is try, and just maybe, make some inroads with other decent people you can get along with even if you disagree with some or most of their views.