We can merge two sorted lists of distinct elements in parallel using the merge path concept:
See https://www.cc.gatech.edu/~bader/papers/GPUMergePath-ICS2012.pdf
and: https://www.researchgate.net/publication/261322325_Merge_Path_-_Parallel_Merging_Made_Simple
Can we do something similar to find the sorted symmetric difference of two sorted lists?
eg. 1,2,3 (symm diff) 0,1,4
gives: 0,2,3,4; notice the 1 disappears since it is common to both lists
Do the following: remove all the duplicate elements from each sorted list. Like if the list is $[2, 3, 4, 4, 4, 8, 8, 9],$ convert it to $[2,3,4,8,9]$. Save the frequency of elements. This can be done in linear time. So now you will have two sorted lists with distinct elements. Do merging as usual, but when two front elements are equal, remove both of them (don't put them in the merged list). In the merged list put the elements according to the frequencies. The resulting merged list will be the symmetric difference.