Can allied pings from specific players be prevented?

At the very first indication of flaming or other very negative chat coming from an ally, I tend to use the mute option. However, muted players don't seem to be throttled c.q. downright muted as far as pinging goes.

Is there any way to throttle or mute pings from allied players? If not that, as a workaround I'd also be happy if there was a way to turn off pings completely.

I've searched, but only found:

• A three month old thread on the Blizzard forums with no recent activity or definitive answer.
• A recent RPS article on "toxic allies", which doesn't talk about pinging at all.
• A Reddit thread "How to deal with noob haters?" with no answer either.

Is it possible at all to stop ally pings? Or is it just not in the game (yet)? A workaround smarter than muting my entire sound would also be appreciated.

Solution 1:

Yes, it is now possible to mute ally pings (as of 19 April 2016) by clicking the mute player pings button on the in-game score screen (opened with Tab).

Solution 2:

No, they cannot be prevented (as of 13 April 2015).

As the game in its current Beta state, you can only block communication to a player in your team from the game statistics menu in or after game. That feature you asked for is not implemented yet. You can always give your feedback about the matter in official forums.

For workaround, if you currently navigate to options menu and then disable all sound for muting pings, then you can use the keyboard shortcut for toggling the sound: Ctrl+S