Once SegWit is implemented, could updated miners still choose to ignore SegWit transactions? Regular transactions can be ignored. What about SegWit transactions?
Transaction selection is up to the miners. The only mandatory transaction is the coinbase transaction (the transaction that collects the transaction fees and pays them out with the block subsidy as the block reward).

Besides that they may select anything between no transactions at all, over only regular transactions or only SegWit transactions, to the mix of all transactions that gives them the most transaction fees.