I suspect the answers would be: use non-arrow keybindings for browsers (e.g. vim-like plug-ins, or alternative keyboard shortcuts), remap your terminals keys (maybe, use a different terminal entirely?), use insert mode for only inserting text.
I use a “vimium” plug-in for Firefox and I quite like being able to go up/down with j/k. Though I still use the arrow keys for my terminal.