Viewers cannot interact with data. So, allowing them to save "their own views" does not make sense since they won't have a custom view.
Viewers can interact with reports. It even says as much on Tableau's website: Tableau Pricing for Teams & Organizations
I don't understand why they can view custom views but can't save their own. If there were any role that saving custom views would be useful for, it would be viewers.
There might be some options available to you for saving Custom Views through this online help guide: Use Custom Views
If this answers/resolves your question, please mark this response as correct so that others might find it useful in the future.
Thanks for the suggestion Don. Unfortunately it doesn't resolve my issue. Creating/saving custom views is a capability not offered to Viewer licenses, only Creator or Explorer. The vast majority of our organization is on Viewer licenses since they don't need to build or edit reports but only interact with them. Having a small subset of our users (Creators) create and save every possible custom view that our audience would want just isn't feasible/scalable. We would rather have our Viewers be able to create and save their own custom views since they are the primary interactors of the dashboards. I can't really understand why Viewers would not have this capability since it doesn't have any impact on the dashboard other than what they themselves would see.
I have exactly the same problem and it is becoming my biggest issue currently. Only thing a viewer wants is to filter out and adjust a dashboard and save it for future use or sharing. I really think it is a shame that Tableau went for a business model that forces you for explorer license even though the only thing a viewer will do is just view and SAVE that view. I am still discussing this with Tableau directly and hoping to have some timeline or a solution on this. So far the recommendation was that we do dashboards that are easier to navigate and minimal so that it is not too hard to filter things again each time. My response to that is a simple bullshit. The whole power of Tableau is that you can merge small dashboards into one with the capabilities it has so you have few dashboards to maintain while they can use clicks and filters to get to what they want and SAVE it! So, I completely agree with you...