Viewing a status without appearing in the viewer list
Turning off read receipts works, and it costs you something in return. The honest trade.
WhatsApp shows status posters exactly who viewed. If you would rather not appear in that list, there is one supported way to do it and several unsupported ones worth avoiding.
The supported way
Settings → Privacy → Read receipts → off.
With this disabled you do not appear in anyone's status viewer list. It applies to statuses specifically as well as to blue ticks in chats.
The cost
It is symmetric, and that is the part people miss: you also stop seeing who viewed yours, and you stop seeing blue ticks on your own messages.
WhatsApp designed this as a mutual trade rather than a one-way cloak. You cannot keep the information while withholding it.
Group chats are an exception — read receipts still show there regardless of the setting.
What does not work
Airplane mode tricks. The old advice was: let statuses load, turn on airplane mode, view them offline. In current versions the view is queued and reported when you reconnect. It delays the notification rather than preventing it.
Third-party "anonymous viewer" apps. These generally want your WhatsApp Web session, which means handing a stranger access to your entire account. The cost is wildly out of proportion to not appearing in a list.
Viewing from the notification. A preview does not count as a view, but it also does not show you the media properly, so it only works for text.
A note on saving
Saving a status does not add you to any list — the viewer list records views, and saving is a local file copy WhatsApp cannot observe. But you have to view a status before the file exists on your phone at all, so the view is unavoidable if you want to save it.
With read receipts off, you can view and save without the poster knowing either happened. Whether that is the right thing to do with someone's photo is a separate question, and one worth actually asking.