For the sake of conversation and distinguishing the two blocks, lets label them BLOCK_A and BLOCK_B
The fact that the merkle roots are identical between BLOCK_A and BLOCK_B would not have any effect on the behavior. It would continue the same as any other time that two miners solve a block at nearly the same time. Specifically:
The portion of the network that received BLOCK_A first would add BLOCK_A to their blockchain. When they received BLOCK_B, they would not add it to their blockchain since they already have a chain of that height.
The portion of the network that received BLOCK_B first would add BLOCK_B to their blockchain. When they received BLOCK_A, they would not add it to their blockchain since they already have a chain of that height.
Then the miners that accepted BLOCK_A would begin working on the next block at height BLOCK_A + 1
Meanwhile, the miners that accepted BLOCK_B would begin working on the next block at height BLOCK_B + 1
As soon as one of these miners solved a block, they would broadcast it. Lets assume for a moment that it is a miner that was building on top of BLOCK _A.
Since BLOCK_A and BLOCK_B are both at the same height, this new block would make a longer chain. All the nodes that had previously accepted BLOCK_A would simply add this new block to their chain after BLOCK_A. All the nodes that had previously accepted BLOCK_B would abandon (orhpan) BLOCK_B and accept the new longest chain BLOCK_A and BLOCK_A+1. The network would converge on this new chain.
I would think that BLOCK_A+1 would be compatible with the chain using BLOCK_B , since they have the same hash and you can chain the blocks together. So therefore, when BLOCK_A+1 comes out and is broadcast, you now have:
chain: BLOCK_A -> BLOCK_A+1
chain: BLOCK_B _> BLOCK_A+1
they would only start diverging if the TXO wouldnt validate, but that may or may not happen on the next block. Maybe I just answered my own question.