This poem can have more than one interpretation. And in this answer I will be providing three readings of this poem:
1) There is the romantic reading which is generally done by reading the text as a work from the romantic period; you can view the elements in the poem as merely romantic element, where the Albatross is just a bird who represents nature, and that the Mariner disrespected nature by shooting the Albatross for no logical reading, and thus he was punished for it and all his crew died by “life and death” which are supernatural elements Coleridge uses as a romantic writer. The Mariner insulted nature by killing the bird and thus nature got back at him and punished him and then he learned his lesson and started to appreciate nature and then he was forgiven and the Albatross fell from his shoulder which can be interpreted as a symbol of guilt off his shoulder. And then after the Mariner learned his lesson he travels and tells his tale to teach others.
2) Another reading of this poem can be a Colonial reading, as in Coleridge meant colonialism in his poem where he used the supernatural elements to show the effects of colonialism. He represented the colonizers by the Mariner, and as for the natives they were represented by the Albatross and when the colonial shot the naïve for no reason it is an act of colonialism but the “main head” wasn’t the one who died for it but his “soldiers” his crew died for his mistake and his greed for colonizing that place. And then the Mariner started to change into an outsider, his skin color changed into a darker one, his language became unrecognized for the English people and thus they considered him to be an outsider, and that is where we can say that the Mariner started to identify with the natives and then started to spread his tale and spread awareness.
3) Another reading is said to be seen in the poem is the reading of Religion, it is said that Coleridge is criticizing religion when the Hermit – which is a word used to refer to a religious figure – comes and sees the Mariner after the Mariner lost his crew and the first thing the Hermit says what are you, not how are you? or are you ok? What are you he asks which is to emphasize on his race and who the Mariner is and that is a criticism on religion because religion is supposedly above racial and ethnical differences. Another religious aspect that is noticed in the poem is when the Albatross is placed upon the Mariner’s shoulders and that is thought to be a biblical refrence to Christ.
Those are the main reading I know and interpreted from my studying of the poem, hope I was helpful.
My Refrence was from a book about England in the 19th century.