Maha Mantra for Kali-yuga:

Hare Rama, Hare Rama, Rama Rama, Hare Hare

Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare

 or

Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare

Hare Rama, Hare Rama, Rama Rama, Hare Hare

Above mantra means:

"Oh God and your energy please engage me in your service"

Why Shri Chaitanya Mahaprabhu reversed the order of Maha mantra begins with Hare Krishna?

Context: First understand from where this mantra is originated......

Read this conversation between Lord Brahma and Narad Muni (from Kali Santarana Upanishad):

At the end of Dvapara-yuga, after traveling all over the earth, Narada Muni went to Lord Brahma and asked him, “Oh, Lord! How will I be able to swim across this ocean known as Kali-yuga?”

Lord Brahma said, “Your words will benefit all mankind. Listen to the essential secret of the Vedic scriptures, which is concealed (like a treasure). By uncovering this knowledge, one can swim across material existence during Kali-yuga.”

“Simply by chanting the name of the Supreme Personality of God head, Lord Narayana, the sole proprietor of all, one’s sins can be eradicated in Kali-yuga.”

Narada Muni again asked, “Which of the Lord’s names should we chant?”

Lord Brahma replied: 

                 Hare Rama, Hare Rama, Rama Rama, Hare Hare

                 Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare

Narada again asked, “Oh Lord! Is there a proper procedure for this chanting?”

Lord Brahma immediately replied: “There is no set procedure for chanting this Maha-mantra. A seeker of truth can chant whether pure or impure—liberation still awaits him. Such liberation can take various forms: as in living on the same planet as the Lord, becoming one of His personal associates, appearing in a form that is like His, or merging with Him.”

When one chants this Maha-mantra of sixteen names three-and-a half crore times (35 million times), he absolves himself from the killing of a Brahmin, assassination of a warrior, stealing gold, or committing harmful deeds to forefathers or other human beings.

By chanting the Maha-mantra, one immediately becomes purified, attaining release from sins caused by neglecting other religious duties. This is the teaching of the Upanishad.

Now go back in 15th century, it was not like today's world. The Vedic mantras are traditionally not meant to be chanted by anyone except Brahmins. Brahmins were considered the only qualified people for chanting Vedic mantras.

Shri Chaitanya Mahaprabhu reversed the order so that the mantra begins with Hare Krishna since the caste conscious Brahamanas of that time (15th Century) became anxious as to why Gaudiya Vaishnavas were encouraging shudras (labourers), women and even Muslims and other meat eaters (even cow killers) to chant the Vedic mantras since the Vedic standard dictate that these mantras should not be given to unqualified persons.

Shri Chaitanya Mahaprabhu, being merciful to all beings, certainly didn't want to offend the Brahmana community so he changed the order so that all can benefit from this great chant and thereby attain their goal of life, love of Krishna, irrespective of their background.

Conclusion:

No matter you are Hindu, Muslim, Sikh or Christian etc etc...these all are man made designations....God is one and you should pray to God to engage you in his service.....