What you could be best doing with that block, would be to create a new block in the admin CP which is a custom block. You can use that as a template, and with doing it this way you can set specific permissions.
So for that popular contributors block for example
Go to Pages->Page Management->Blocks in the admin CP
Click "Create new block"
Under "Plugin" select "Popular contributors" and click next
Give it whatever name you wish in the name section, then click save
Remove the permission for guests, and click save
Now you have created a custom block, you can add it to the front end
Open the block manager on the page
Drag the "Pages->Custom blocks" block to the page
Click to edit that block and choose the custom block you created
In this way you can create any number of blocks with exactly the permission you wish