How to make the browser back button disregard hash tags?

That's intentional browser behavior, and is the proper use of hash tags. As a result, I suggest considering whether the javascript that is using those hash tags is the problem, and to change it to a different storage method. Effectively, you can just use a globally available javascript variable for that purpose, because no page reload will be happening so the variable will persist.

window.stage = 'start';

// Another stage
window.stage = 'onfire'

You'll still want to suppress the standard behavior from clicks for js elements, of course.

Alternatively, if you want the stages to be stored, but not "navigatable", you can consider using localstorage on more modern browsers.

EDIT: (based on the new information)

The thing that you are trying to do is an extremely common scenario in webdev because pages don't save much by way of their user's state/information.

You want to store information about what your users have completed, what stage they are at in a process. Even when they have navigated away from a page.

There are somewhat limited number of places to "store" data: the hash, localStorage, cookies, or client-side, and that's about it. If I were a user of your page, I suspect that I would want my data stored regardless -how- I navigate through your app.

So I suggest considering a better location for storing the state of your webpage than the hash, which is generally designed for navigation. If they're going to be logged in via php, just store it via php to the database. If not, then store it to localStorage where available and fallback to cookies, or just use cookies.

Your end navigation may look as tangled as this: start page > processing page > any other page > processing page > leave the site > return to processing page

But each time they return to the processing page, their

You can count how many hashes you've clicked since you've loaded the page, then use that count with history.go( - countHashes) to go back to your page.