[Ger-Poland-Volhynia] a little Mennonite help, please?

[Dale Mattis]

I'm researching my SAWATZKI/BAST branch, which came to Michigan around
1870 from an area near the West/East Prussia border, around Gulbein,
Sommerau Parish, Kreis Rosenburg.

This branch was Lutheran here, but I'm told that SAWATZKI is a fairly
common Mennonite name.  A friend has found some Sawatzki names in the
parish records in that area in the 1800-1850 timeframe.  I'm unfamiliar
with Prussian research - would parish records in that timeframe include
Mennonites?  Would there be an annotation of some type to delineate
Mennonites (or any religious affiliation)?

Any help would be appreciated.  Thanks in advance.  Dale