As I understand it, they will drop all controversial parts of the Bill and only proceed with non-contentious issues. They do not have time to debate controversial issues. It is only at second reading stage which is relatively early on. If the Party Whips are deciding things, I think that means just Labour and Tory as they do not have much regard for anyone else!
We had a similar situation with the Child Poverty Bill this week and the Equality Bill is also going through the same process. Although they were further on.
I will certainly keep an eye on what is happening.