While it's certainly true that atheists frequently do attempt to uphold the separation of church and state, I think it stands to actually see if they're the most frequent belief system pushing for it, or if, in fact, those of theistic beliefs do so even more frequently.
To answer this question, I found a list of court cases concerning church/state separation. I limited my inquiry to those that actually reached the supreme court since many earlier ones that never did stood to be overturned or were eventually consolidated with others. In chronological order, here's my findings:
Everson v. The Board of Education of the Township of Ewing
Torcaso v. Watkins
Engel v. Vitale
10 parents of which an unknown number were religious
Epperson v. Arkansas
Abington Township School District v. Schempp
Unitarian (consolidated with Atheist in Murray v. Curlett)
Lemon v. Kurtzman
Wisconsin v. Yoder
Amish (supported legally by a Lutheran lawyer)
Wallace v. Jaffree
Edwards v. Aguillard
Various teachers, parents, and religious leaders
Lee v. Weisman
Santa Fe Independent School District v. Doe
Mormon & Catholic
Zelman v. Simmons-Harris
Elk Grove Unified School District v. Newdow
McCreary County v. ACLU of Kentucky et al.
7 plaintiffs of unknown religious affiliation
Kitzmiller v. Dover
11 parents of which an unknown number were religious
Van Orden v. Perry
So it turns out that of 8 of the 16 cases involved those with theistic beliefs as plaintiffs.
(NOTE: I have included those cases which say something to the effect of "an unknown number of which were religious". In my searching I found that articles would not specify how many of the frequently multiple plaintiffs, held a religious affiliation.)
When we count the number of cases started by atheists, we find that only two cases fit this criteria.
The rest of the cases (6) I couldn't find any information on the plaintiffs (
If anyone knows of the religious affiliation of the cases I have marked as unknown, please let me know so I can update the information).
So looking at the breakdown from these 16 cases, 50% of cases reaching the Supreme Court are started by people with religious affiliation. Only 11% are not. The remaining 39% were undetermined.