Do you want the red lines to meet the blue line at the point they currently cross?
Hmm, there isn't a build in transformer that will move the entire feature to snap to a line.
I would try something along the following:
Assign unique ID (UID) to each red feature.
Extract endpoints of each red line (if you know that's it's always the start vertex that should be snapped to the line then just extract that)
Neighbourfinder (red points, blue lines) to get the the closest candidate x/y
If you extracted both end points keep only the one with the smallest distance to line (per UID).
Calculate the offset between the vertex x,y and the closest candidate xy
Join the attributes of the red point to the red line (by UID)
Use the offsetter with the values calculated above.
A similar approach to @jdh except I've assumed that the lines should be shifted so they meet at the point where they currently cross the line
You probably also want to think about whether you want to shift in different directions depending on whether the start or end point of the line is closest
offset_lines.fmw