B737 First Officer reported receiving a Flight Control Master Caution for Feel Differential Pressure and low hydraulic quantity indication during climb out. Flight crew diverted and landed safely.

Narrative

During the initial climb-out from ZZZ; we received a Flight Control Master Caution for Feel Differential Pressure. It came on and subsequently went away three separate times. We referenced the QRH and continued normally. After leveling off at cruising altitude; I pulled up the hydraulic quantity/pressure page due to the aforementioned Master Caution; and found that the Sys A Hydraulic Quantity had gone down from approximately 95% to 78%; with both Sys A and B at 95% indicating both on the ground in ZZZ and in the air on the previous flight with the aircraft (Kept the aircraft for both legs that day). We jumped into the FM; and noted factors that can cause fluid displacement; and deduced that calling Maintenance Control would be prudent. Maintenance control told us to monitor the situation for 10-15 minutes; and that they would continue monitoring the frequency we were on with them. In that time; the Sys A fluid quantity continued to decrease from 78% to 71%; and after advising Maintenance control once again; they recommended a diversion to ZZZ1. We looked at all factors; and because there was a cold front producing a significant line of weather that we would have to deviate around going to ZZZ1; that ZZZ2 (Prior to the weather system) would be the safer alternative; as we communicated that if the quantity continues to drop; while deviating around some nasty weather; there is a potential for the situation to be much less safe. I noted the Swiss cheese model" of contributing factors that had already been "lining up". Out of abundance of caution; we [requested priority handling] after communicating with dispatch. The fluid quantity indication continued to drop on the descent/approach into ZZZ2; but landed uneventfully. After clearing the Runway; I communicated with Crash/Fire/Rescue to check the aircraft for any potential fluid leaks. None were noted; so we taxied to the Gate. The crazy thing- after clearing the Runway; both Sys A quantity showed 95%; right where it was when we left the Gate in ZZZ. After maintenance in ZZZ came onboard; they suspected it was a faulty transducer. The Captain and I led a thorough debrief; and deduced that with all factors/available information; that our course of action was the safest given the scenario; especially given Maintenance control's input that the indications we were receiving were not normal for our given phase of flight. The [priority handling] out of abundance of caution; with our headspace at; "If we are losing fluid; and have lost >25% up to this point; there is a potential for extreme fluid loss in the approach/landing phase; with flight control displacement/flaps/gear". We called the Chief Pilot in a prudent timeframe; and after a 25 minute conversation with them; they decided to remove the Captain and I from the next flight due to human factors reasons; they stated. We received necessary rest at the hotel in ZZZ2; and the rest of the pairing continued uneventfully."