Those passages do indeed bear upon this topic:

Phillippians 2:2-3  "Fulfil ye my joy, that ye be likeminded, having the same love, being of one accord, of one mind.  Let nothing be done through strife or vainglory; but in lowliness of mind let each esteem other better than themselves."

Striving for equality within the body of Christ is hardly Paul's prescription here, more like the opposite.

As for James in chapter 4:5 "Do ye think that the scripture saith in vain, The spirit that dwelleth in us lusteth to envy?"

Envy is the seed of covetousness. It was equality that Cain lusted after.  Striving for equality - seeking it in death.   

About Gal. 3:28-29... In Christ: We are all EQUALLY heirs to the promise.  We are all EQUALLY delivered from the body of death by Christ's death and resurrection.  The text has nothing to say about seeking equality within the church.  To say it does is forcing the interpretation.