I see a lot of SR5H basses being played in country music. Does anyone know if there is a consensus among the pros using them if they prefer the serial or parallel pickup setting?
I don't know either what kind of sound you like or what kind of amp you play.
Both sounds, serial or parallel, do sound fine. Series mode will give you more low mids and a bit more volume, more balls, parallel mode a bit more clarity and the so called Stingray signature sound.
Depending on your amp, cab and eq - setting both sounds plus the third option, coil two plus dummy coil (on newer SR 5 it's coil two plus filter), will sound fine and fit into your personal style of music.
I am a working musician and use my Rays (4 + 5 + 5 Classic) in several bands from a 80's / 90's Heavy Rock Coverband over two Heavy Metal Bands and a Soul / Blues Band. Depending on the amp and eq settings the basses just sound right.
Try it out. Your have choices to do.