They haven't made an official statement as to whether they will credit SegWit2X or not to their users as far as I know.
But from what we have seen in the past, they will most likely do.
That was the case with Bitcoin Cash. You can also read their recent statement on Bitcoin Gold:
https://support.bittrex.com/hc/en-us/articles/115002320451-Statement-on-Bitcoin-Gold-BTG-Bittrex will make all reasonable attempts to credit our users BTG but until we have a fully supported wallet, we can neither guarantee tokens or consider creating a market. We will continue to monitor the state of the codebase and network. We'd also like to encourage the BTG development team to reach out to us.
Don't be so sure! They said that they will support bitcoin gold and in the last minute they changed their mind and did not supported the new coin. I moved my holdings to them to receive the new shares based on their initial announcement and my BTG coins got lost.

It's a sh*tty move to "change' their mind the last second. Leaving everyone in doubt while keeping your btc on their exchange.
What is stopping them to use your BTC to claim the BTG without you ever knowing?
It's the same with cryptopia, they didn't support the Bitcoin Gold. But what is stopping them to use your bitcoin to collect bitcoin gold, without you ever knowing?
I guess that would be the biggest reason why they didn't want to support the new bitcoin.