Hi there,
Thank you for reaching out.
We have received reports of this soft lock you're experiencing. At this time, the underlying cause of it is being looked into by us. Your patience and understanding while this is ongoing is appreciated.
For any updates on this issue, we recommend viewing our Patch Notes as they become available, posted on the [url=https://www.bungie.net/7/en/News]News[/url] page.
Little bit of a temporary workaround
Remove both renegade abilities from being equipped and then restart the mission
It'll trigger the original dialogue and when spider finishes talking, the ship will open.