I don't have the app and I use reddit (although not often) via my mobile browser (firefox) and it never forced me to download the app, as far as I recall.
It does it occasionally to me (Safari on iOS). When it happens, I just close the page. I hope this is enough of a signal to make someone think.
I land on Reddit every couple of days or so, and if they don’t kick me I read the thread and sometimes browse a bit a couple of subreddits I used to participate in.
Another Firefox for Android user here. I get popups nudging me to install their app all the time.
Old reddit still works, images and videos are usually forced to go to new reddit. You can sometimes get around it by clicking on the comments link.
I started getting a blocking overlay telling me to download the app on new reddit and I just leave.