1) Exposures are fairly short and frequent and so pixels contaminated by these satellites can be easily rejected. 2) There is a huge amount of resources (relative to other projects) going into the image pipeline for this project.
I don't actually know in details how much this will affect other types of observations though. [2] is the IAU's statement (that goes with that image), which points out some types of observations that might be more affected.
[1] https://www.lsst.org/content/lsst-statement-regarding-increa... [2] https://www.iau.org/news/announcements/detail/ann19035/