The doctrine is that a christian should not get involved in politics. What does that mean?
I realize that question is not asked to know Watchtower's explanation. But explanation and understanding are different. Watchtower's explanation of this issue is so convoluted that it leaves a person's head spinning. But understanding Watchtower's position is as simple as a careful review of history.
The whole thing is rooted in a doctrinal position Watchtower formed in the very early 1940s and termed "neutrality" doctrine.
There are thousands of experiences of JWs refusing military induction based on this neutrality doctrine. JWs could register for induction. That was no offense under the neutrality doctrine. JWs could show up for induction into the military if they were called up. That was no offense under the neutrality doctrine. JWs could undergo the physical prior to induction. That was no offense under the neutrality doctrine. But when it got to taking the oath of allegiance to the government, that was the point at which JWs had been taught it would be a violation of the neutrality doctrine and it was at this point that JWs refused. (See United States v Smith 1942) What Watchtower's upper leadership was not telling the rank-and-file JW is that every one of the organization's top leadership had already been pledging the national oath of allegiance to the United States' government, and continued to do so afterward for decades.
Then Malawi comes along, and the poor JWs over there were being told by leaders in Watchtower that it's wrong to pledge allegiance to any county and that accepting and giving 25-cents for a blank (BLANK!!!) MCP card would be an act of allegiance to the county of Malawi, so the Malawian JWs refused and suffered horribly as a result. During the whole decades long episode top Watchtower leadership were pledging the national oath of allegiance to the United States government. The Malawian JWs had no idea of this gross hypocrisy.
In Malawi it was most certainly not a political act to had over 25-cents for a blank (BLANK!!!) MCP card. The very idea is ludicrous. It's no wonder that to this day Watchtower has never, ever published the inside of the MCP card for JWs to see what this card is all about. Instead it wants JWs to judge "the book" by its cover alone. That's why we find Watchtower has published the front view of this card on two occasions but never the inside. Then JWs would learn the whole story is a religiously motivated hoax.