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Click a link and use window.open() blocks one of the links

I'm trying to create a simple JS function that will open a new window/tab when clicking a specific button, so the user will actually open 2 windows/tabs, however no matter what I do, one of the links gets blocked by Chrome as a "popup-blocked".
I'd like to do something like this:
$(document).ready(function(){
$("a").mousedown(function(){
window.open("https://stackoverflow.com/","_blank");
});
})
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
Click Me!
;
But when I do this, the button link doesn't work, but the JS does.
If I change the JS and add a setTimeout() to it, the button URL goes through but the JS gets blocked.
No matter what I do, I can't get both of them to go through.
Any help would be appreciated.

Navigating to two places at once, with one in a new window, is really popular with people who want to show the user a massive advert in a new window.
Massive adverts are unpopular with users, so browsers take steps to prevent this behaviour.
Sometimes legitimate uses get caught in the crossfire. Blame the blackhat end of the advertising industry.
You'll need to find some other way to display… whatever it is you want to display… to the user that doesn't involve navigating to multiple webpages at the same time in separate windows.

The problem is caused by the mousedown() event you are using which is a part of down+up sequence to trigger the click() event of the <a> tag.
so opening a new window "breaks" the flow and browser is not tracking for the mouse-up event anymore to follow the original url.
so the solution is to attach the click() event instead without stopping propagation. this will fire the attached and original events and none of them will be blocked.
$(document).ready(function(){
$("a").click(function(){
window.open("https://stackoverflow.com/","_blank");
});
})
you can try sample on this page as stackoverflow snippet is sandboxed and is blocking popups

Function repeats on mouse action

I'm setting up an introduction to using Javascript in Adobe Animate HTML5 Canvas for a course I teach. Honestly I haven't done any work in that myself but I've done a bit of Actionscript gaming as well as some Javascript programming outside of Animate, so I'm not entirely clueless.
Part of the exercise is to have a button that opens a URL. It does, but it opens many tabs of it. I'm nto sure how to limit it so it only opens one tab of the URL.
Here's my code. Thanks for your help:
this.urlBtn.addEventListener("mousedown", openPage.bind(this));
function openPage(event) {
window.open('http://www.cartoonthunder.net/', '_blank');
}

mousedown fires while the mouse is down over the element, so it'll happen repeatedly.
Use click instead and it should only fire once.

Is it possible to simulate browser click events?

How can I simulate exact behave of mouse click on a browser's button (e.g. Firefox)?
When user clicks on a button using mouse click then an event is generated. Could I use or call the event manually?
I can use Javascript to simulate click on a button but it will not call the same event in the same way as when a user really clicks on the button.
The reason I ask for solution: record engine for recording any event occur in the document level works in background, I want to create web app with self play functionality, that means when I browse the web app in browser it will do business flow automatically and then the engine will record the events.
Please ask if my question not clear, Thanks.

This is easiest with something like jQuery.
//listen for clicks - real or simulated
$('#some_element').on('click', function() { alert('click!'); });
//simulate clicks (two ways)
$('#some_element').click();
$('#some_element').trigger('click');
It is possible to know, from inside the event callback, whether the event was real or simulated. I did a blog post on this some months ago.

You should look into Selenium. It uses automation and other native APIs to simulate user input in exactly the way you wish.

Using BOTH Href & click listener

I've got a browser plug-in I'm working on and I want it to behave a certain way when the user clicks things. Not limited to, but including, a behavior for links!
The problem is that the plug-in has to work for a wide variety of sites, and some of those sites use the dreaded pseudo-protocol such as:
Show Element
Currently my behavior is added to the anchor tag via
anchor.addEventListener('click', superAwesomeFunction);
Unfortunately this has a problem where the click listener only fires once. If I preventDefault() of course the click listener sticks around, but I've now broken the host site! Otherwise, clicking the link fires the click listener but only on the first click. I'm wondering why my superAwesomeFunction() doesn't fire again if the link is clicked a second time. Is href="javascript:things()" doing more than I know?

It is possible to add an event listener to a link that has a JavaScript function call set in the href attribute.
Here's a jsFiddle that shows it working. Both functions fire each time the link is clicked.
There must be something else going on with your code beyond what we can see in what you gave us.

If you must wait user some time and going on url then, you may add some code to your superAwesomeFunction's process end:
document.location.href = $(this).attr("href");

JavaScript click event

My browser (firefox) prevents any popup from loading, and loads links that open new windows in the current tab, unless I explicitly say I want the link to load on a new tab or window, with the appropriate shortcuts (for example, middle click on the link, or left click with ctrl pressed causes the link to open on a new tab, and shift + left click on a new window).
I would like to create a javascript function f() that runs some code (meant to create the link address) when the link is pressed, and then loads the link that has been created, without removing the user experience described above.
Right now what I have is something like <a href="javascript:void(0)" onclick="f()"/>, but middle click doesn't work (it instead loads the url javascript:void(0)) and neither do the other features described above.
Do you have any idea as how to solve my problem ?
Thanks.

have you tried window.open('url')?
see: http://www.javascript-coder.com/window-popup/javascript-window-open.phtml
Also, as far as I know, you can't control whether or not the browser opens in a new tab or new window. That is a browser setting that is different for every user.
You might also try removing the onclick, and using
EDIT
There seems to be issues with using middle click with opening new tabs instead of executing the javascript: middle click (new tabs) and javascript links
As that site says, you can instead create an id for the element and bind it through javascript.
**Taken from that link:
...
And then in your JS, hook the link via it's ID to do the AJAX call.
Remember that you need to stop the click event from bubbling up. Most
frameworks have an event killer built in that you can call (just look
at its Event class).
Here's the event handling and event-killer in jquery:
$("#thisLink").click(function(ev, ob) {
alert("thisLink was clicked");
ev.stopPropagation();
});
Without jQuery, it might look like this:
document.getElementById('thisLink').onclick = function(e)
{
//do someting
e.stopPropagation();
}

Other browsers may vary, but by default Firefox doesn't tell the web page that it has been middle-clicked (unless you set the hidden preference to enable the feature). You might be able to create a workaround based on the focus and/or mouseover events instead.