Is there actual consensus on the blockchain's tip or only until the next block? Using this scenario https://bitcoin.stackexchange.com/a/40435


  Let's say we have two competing blockchain tips: They both start from
  Block A as a parent, but then there are two different blocks found at
  the same time: Block B1 and Block B2. Both blocks have the same
  difficulty level, and as we learned above this is independent of when
  exactly they were found. Therefore, the total difficulty of Block A +
  Block B1 = Block A + Block B2. One of the two chains will have a
  greater total difficulty once either Block C1 or Block C2 will be
  found.


Is there consensus on the tip being B1 or B2, or only until C1 or C2 is found?  If 2 blockchain explorers have both B1 and B2, can they randomly choose either to be the tip of the blockchain and both would be deemed to be correct?
No, there is no consensus until the next block is found. The network is experiencing a blockchain-fork. It will only mend once one of the tips pulls ahead by adding another block. Then all nodes will reorganize to the longest chain and consensus is reestablished. The losing chain becomes an extinct branch – valid but not part of the longest chain.

There can't be consensus before because from a node's perspective there is no way to tell reliably which one of the two blocks is more popular in the network. They could ask around, but would get mixed answers and could be deceived through a sybil attack anyway. Therefore, nodes accept the first valid block they hear about as the current blockchain tip until proven otherwise – the only valid proof being to be shown a longer chain. They'd still keep the competing block though, and propagate if it is later needed for a reorganization.

In fact, such blockchain forks can even persist for several blocks when competing blocks are found subsequently. E.g. in 2012 there was a blockchain fork with four blocks.

During a blockchain fork, there is a higher risk of doublespends because the competing blocks at same height may confirm different transactions. However, if they occur from natural random chance (instead of an attack), they would be working from the same set of unconfirmed transactions and should contain a mostly matching set. As each blockchain tip considers the other not to be relevant, they do not split transactions to be confirmed, but both try to confirm the whole set.

So, yes. Both are valid blockchain tips, either may turn out to be part of the longest chain in the long run, but a good blockchain explorer should maybe show both until it is clear which one will remain part of the longest chain.