A regular Bitcoin address of the form `1LoD3JXVckEKkZh8nkSrvmQaovnGYu8fNP` is non-private, everyone knows this. Posting such an address in your public profile allows blockchain data harvesting firms to learn when your address receives BTC and from where, and to whom your address sends money to.
But there is no reason to post such an address. If Alice wants to post a fully private Bitcoin address that can't be monitored by data harvesting firms, she should post a stealth address [1]. If Bob wants to send Alice BTC, he takes Alice's stealth address and derives from it a regular Bitcoin address. No one but Bob can know what Alice's derived Bitcoin address is, because the address is derived from Bob's private data.
The libbitcoin software suite supports these stealth addresses, but because libbitcoin isn't VC backed and doesn't have the hype of moneyed interests behind it, libbitcoin wasn't good enough for Keybase. They probably never even evaluated it.
A ZCash "zaddress" is basically just a Bitcoin stealth address.
That the CEO of a privacy-focused social networking service is not in tune with this information is a huge red flag to me. As each Keybase.io profile is an implicit endorsement of Keybase and by extension Keybase's investors, I was deeply saddened and frustrated to learn the news that Keybase has decided for its entire userbase to prop up ZCash based on their faulty assumptions.