B737 MAX 8 Captain reported an Oil Filter Bypass Light illuminated in flight. The flight crew shut down # 2 engine; continued to destination airport; and made a safe landing.

Narrative

Approximately 50 SSE of ZZZ1; FL340; we observed an Oil Filter Bypass caution light on the #2 engine. I elected to let the FO (First Officer) keep flying while I got out and read the QRH. The caution light was unusual in that it flashed as expected; then behaved erratically. It would momentarily come on and stay on; then flash; then go out; and then flash again. We discussed that it could be an indication problem since all other engine instruments read normally; but since we had the light we would run the checklist. The FO slowly retarded the #2 thrust lever; and when it reached idle; the light went out. I requested a lower altitude from ATC; they cleared us to FL240; and the FO brought up the engine out Cruise page; which indicated a max single engine cruising altitude of FL246. The FO started a -1000 VVI descent using Vertical Speed. We quickly both agreed that we should continue to ZZZ to land and anticipated a gradual descent all the way there. About that point one or two minutes had passed; the Oil Filter Bypass light came on again and stayed on. Before shutting down the engine as directed by the QRH; I called the FAs (Flight Attendants) and told them we were going to shut down the #2 engine; not to be alarmed; to follow normal procedures in securing the cabin; that we were going to land at ZZZ and taxi to the gate to deplane; and that I would make a PA to the Passengers.We continued running the checklist. I was surprised how much adrenaline I felt in my body; and knew I was in the Yellow thinking about what was being done and looking ahead at what had to be done and the various considerations in accomplishing all this. I commend the FO in helping maintain excellent CRM as he asked me to slow down the reading of the checklist so he could keep up and not rush things; and helped ensure we used proper response-response methodology and proper guarding of all switches. After starting the APU; I was impatient in waiting for it to come online and read ahead to see the next steps. We started balancing the fuel; put the transponder in TA; and verified the isolation valve switch in auto. By that time I'd forgotten about the APU start sequence; and it wasn't until later in the descent as we crosschecked everything that I'd forgotten to connect the APU to the #2 side. When discovered; I reached up and connected the APU to #1 and #2. When the autopilot disconnected; I once again realized I was rushing a bit. The FO politely reminded me to not rush. We reconnected the #1 generator; and everything else looked accomplished properly.I [requested priority handling] with ATC and told them we planned to land at ZZZ and taxi to the gate. I gave TRACON the requested information. I sent a message to Dispatch informing them of the situation and our plan to land in ZZZ. They acknowledged.I then made a PA to the Passengers. Later; when debriefing the FAs; they appreciated the heads up call which made them a bit flustered due to never experiencing an engine shutdown before; but also gave them a clear understanding of the plan. They debriefed that I sounded extremely relaxed on the PA (which I'm glad for since I wasn't feeling relaxed); and that all the Passengers were very calm. There were no Passenger concerns noted throughout the event.After the PA I discussed with the FO everything we had done (I believe this is when we noticed the APU error); quickly reviewed everything and asked if there was anything we'd missed. We couldn't think of any. I ran the one engine inoperative landing checklist through the Approach Checklist. The FO verified brake cooling did not require any special procedures. I then took control of the aircraft for the final descent; approach; and landing.It was a nice VFR day with gusty winds. We were cleared the Visual to XXL. I'm grateful for our simulator training. Flying a single engine approach in the SIM is harder than the approach I flew. The MAX -800 is a stable; smooth aircraft. And; although it felt odd flyinga single engine flap 15 visual approach; the aircraft flew nicely and handled it well. We landed and taxied uneventfully to the gate.We debriefed Maintenance on the event and put it in the logbook. I then had many phone calls with [company representatives]; debriefing them of the events. It was concluded the safest course of action was to pull us from the trip and send us home. I agreed with that decision. I've had plenty of adrenaline flying moments (low visibility crosswind landing in spring blizzard); but the adrenaline always dissipated after 30-45 [minutes]. I was surprised how stressed my body felt. It wasn't until I was driving home over four hours later that I started relaxing. That was a first for me.I want to say; again; how well the FO did flying the aircraft and reinforcing excellent CRM as we worked our way through this event. Except for my mistake with rushing the checklist and jumping ahead with the APU; I think we worked very well together bringing this flight to a successful conclusion. I commend the professionalism of ATC; [airport] personnel; ZZZ Station Personnel; Operations Personnel; and (Union). Everything they did was appreciated.