Prevent window.onhashchange from executing when hash is set via JavaScript

You could reset the variable from the event handler itself:

var currently_setting_hash = false;

$(window).on("hashchange", function() {
    if (currently_setting_hash) {
        currently_setting_hash = false;
        return;
    }

    currently_setting_hash = false;
    //...
});

currently_setting_hash = true;
window.location.hash = "#abc";

Since the event is delayed, there is the possibility of events occurring in a different order than you expect (e.g. imagine the user changing the URL by other means either immediately before or after your code does). It is important to make sure that you do not become inconsistent by assuming the event is yours. Therefore I have a suggestion (based on your code and Adam Bubela's):

var expectedHash;

window.onhashchange = function () {
    if (window.location.hash === expectedHash) {
        return;
    }
    expectedHash = window.location.hash;
    // ... do actual reaction to change here ...
}

function changeHash(hash) {
    hash = canonicalizeHashValue(hash);
    expectedHash = hash;
    window.location.hash = hash;
}

// Helper - return the version of the URL that the browser is expected to
// so that the equality test is accurate.
function canonicalizeHashValue(value) {
    // Borrowing an A element's ability to resolve/parse URLs.
    var tmp = document.createElement('a');
    tmp.href = "";
    tmp.hash = value;
    return tmp.hash;
}

This code will suppress the change handler only if the change is to the value you are expecting. (The assignment inside of onhashchange makes sure that the handler also runs if the hash temporarily goes to another value, which I assume is more correct than the alternative.)

The third helper function canonicalizeHashValue is needed only for precision in case you are specifying a non-canonical value, e.g. changeHash('foo') instead of changeHash('#foo').

If you want to use just plain Java Script:

    var currently_setting_hash = false;

    window.onhashchange = function() {
        if (currently_setting_hash){
            currently_setting_hash = false;
            return;
        //...
        }
        alert('outside the script');
    }
    function changeHash(hash){
        currently_setting_hash = true;
        window.location.hash = hash;
    }