Technically, there is no reason why the two protocol upgrades couldn't be added to a blockchain in combination. Obviously, they would have to be amended for compatibility in their treatment of blockweight/blocksize. The perceived incompatibility mostly stems from the radically opposed visions the two developer teams appear to have regarding the scaling roadmap of Bitcoin.
SegWit was especially engineered to provide a capacity increase in a way that does not require a hard fork. Many of its proponents appear to expect a hardfork to permanently split the Bitcoin network.
The Emergent Consensus proponents on the other hand appear to take the position that hardforks are preferable to softforks or at least perceive them as much less risky.
Neither of the teams appears to perceive the other proposal as a priority for inclusion into the codebase. A bridge proposal was provided by means of the "BitcoinEC" client that patched the Emergent Consensus feature on top of Bitcoin Core 0.14 which doesn't appear to be maintained anymore though.