Ok, this is definitely unusual — sorry for the difficulties! It’s possible this is from a conflict with another plugin or the theme, but I haven’t seen a problem quite like this, and normally, the firewall option is already turned on in a new installation.
Usually, I think the only option that would cause the options page to refresh like that is the “Live Traffic” option — were you trying to also change that one? And can you try going to the Live traffic page under Wordfence’s menu, and turn off Live Traffic there, using the slider at the top of the page? If that setting “sticks” when you change it and leave the page, then that rules out some issues. (This is the same option as the checkbox “Enable Live Traffic View” on the Options page, so that should change as well, if this works.)
You can also try viewing the javascript console (while on the Options page) to see if there are any warnings, which are sometimes a sign of a plugin conflict. Here are instructions in case you need them:
Open the javascript console
If none of these help, I would recommend turning off other plugins temporarily, and checking if the Options page works then. If it does, then you can turn on one plugin at a time and check the page in between, to find out which one is causing the conflict. Let us know if this helps, or if you still have trouble.