On one level she is observing how in life we are all part of the same procession which ultimately leads to death, but she is also making an observation about class in that even the most “purple” (royal) and “ermine” trimmed nobility are headed to the same fate as “simple You and I” and that a poor person’s “escutcheon” (which she spells “escutscheon”) is as valid as the king’s.
I love the image of “One mitred afternoon” because not only is she using afternoon as the time of life when our own sun will begin its dip below the horizon of mortality, but you can almost see the sun shining through the clouds, lighting them up like a golden ‘mitre’ in the air. It’s a wonderful image. Her use of “purple” enforces this imagery by adding more color to the scene while also building up the image of royalty and wealth.
The second stanza is remarkable in how on the one had she describes a procession of a royal dignitary processing through a city as the crowd cheers and strains to get a better look at them, but she also has put all of humanity into that “Coach” and “we ride grand along” together. She’s showing that we’re all on the same ride, we’re all passangers in the same coach and she enforces this solidarity with the line “Chamber, and state, and throng” to make the connection between the king in his “chamber” who leads the “state” which is made up of the “throng” of people.
The third stanza is about duty and she uses the words “attendants”, “service”, and “loyally” to describe that all of us are in the service of only king which she described in the first stanza as the one whom “none [can] evade this crown”. Yet she is not saying that there is such a massive gulf between God and humanity because she continues her hat metaphor to describe how even the lower classes raise their “hundred hats” – the poor also wear a hat like the bishop (who wears the mitre) and the poor (the “simple You and I”) even have their own “meek escutcheon” (coat of arms / family crest) just as an earthly king does. We all wear a hat: the King, the poor, and even God with his “crown” and so we all have that in common.
In the end we all come to the same fate, but she isn’t necessarily making a case against being rich in favor of being poor, rather she paints a picture of life as a parade and celebration in the afternoon under a blazing sun in which we all come together as best we can and “claim the rank to die”. She is not judging class, she is merely inviting everyone to the same party regardless of their circumstances.