How is Lewis Carroll's christian life reflected in his works through symbols and themes?
The entire book is a mockery of the systematic impulses of Christianity and the Catholic Church. The instances of "directives" given to Alice (drink me, eat me) are specific references to the body and blood of Jesus within Catholicism (Holy Eucharist) and that without any further direction or proof of resolution she does both.
The scene of the tea party involving the Mad Hatter (most likely the Archbishops), the Hare (Priests), and the Dormouse (monks) is a mockery of the institution of the Church - references to the repetition of the movement from seat to seat, the reference to "Time" and of course inferring the Queen has "condemned" the Mad Hatter to continue his pattern due to his inability to "Repeat" a specific nonsense rhyme (liturgy, prayers).
Alice's run in with the Caterpillar and the Caterpillar's insistence on Alice "confiding and confessing" to him who she is and why she is there are direct commentary on the church's implementation of confession or penance.
Alice's involvement with the Cheshire Cat (now you see me, now you don't - have faith/belief in something you cannot see) can be associated with Faith in a higher being, specifically the Catholic God.
My favorite though is Carroll's commentary on "baptism" of a baby - the use of the pepper in the kitchen of the Duchess as a holy water, anointing a baby in order to accept the baby into the church (purpose of baptism) when all the while the baby is grunting (its inability to communicate whether it believes and accepts Christ). The Duchess (the mother of the baby) hands the baby over to Alice (symbolic of a godmother within Catholic Baptism) who leaves the house with the baby and presents the baby to the talking frogs (another personification associating animals with the priesthood). After a bit of time with her god child, Alice scolds the baby for grunting and not communicating correctly only to find out the baby is really a PIG!