Is there actual consensus on the blockchain's tip or only until the next block?
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.