git rebase --continue no changes

If I understand correctly, when you're getting the merge conflict, you're accepting all the changes from branch_1, meaning that that particular commit from branch_2 is irrelevant - any changes in that commit are identical to the incoming changes from branch_1.

When git is saying

No changes - did you forget to use 'git add'?

it's telling you that the commit you're trying to apply doesn't make any changes to the repo, and therefore there's no reason for it to exist.

The simple solution to that is git rebase --skip, which just says "ignore this commit and move on" as suggested in @C-Otto's comment. This will skip the commit you're currently dealing with, and move on to subsequent ones.

You might also find it easier to use interactive rebasing (git rebase -i), which first presents you with a list of the commits it will apply, and gives you various options for what to do with each individual commit. In this case, if you identify a commit that is no longer relevant, you can skip it up-front, so you'll never see the conflict in the first place.