You can hide your balance figures on screen. On the mobile app, tap the balance at the top of the Home screen. It is masked, and a message reads "Balance hidden. Tap again to unhide". Tap it again to show it.
Tapping the balance on your Portfolio chart does the same.
While hidden, your own figures are masked across the app on that device: the Home screen, your Portfolio and perps account values, your own profile, your cash balance sheets, your trade rows, your position on a token page, and your own row and rank on the leaderboard.
Other traders' figures are not affected, and neither is your row in a token's holders list.
On the web app, hover over your profile picture at the top of the page and choose Blur balances from the menu, or press Cmd+B (Ctrl+B on Windows).
This is a display setting saved on the device you set it on, not on your account. Another device or a fresh install shows balances again, and nothing in your wallet changes.