Yes. YNAB is a web app with no desktop program on any system, so it works the same on Linux in Firefox or Chrome with your budget and phone apps untouched.
YNAB by You Need A Budget · Money & tax · Works in a browser
YNAB lists itself as running on iOS, Android and the web. There is no installed program for Windows either, so
there is nothing you are giving up by moving.
Sign in at ynab.com in Firefox or Chrome and your budget, categories, accounts, targets and reports are all
there. Bank imports keep working because they happen on YNAB's side, not on your computer. Your phone app carries on
as before, and your subscription covers the account rather than a machine.
Most browsers will let you install the page as its own window from the address bar menu, which gives you a YNAB icon
in your dock and a window without browser clutter.
The only real catch is that you need a connection to use it, which was already true on Windows. If you would rather
keep your money on your own computer and stop paying a subscription, the envelope-style budgeting YNAB does is
something HomeBank and KMyMoney both offer, in plainer clothes.