Here's what Matthew Henry's Commentary has to say on these verses
(this commentary was written in the early 18th century, so some of the wording may sound out of place.)
Phillipians 1:15-18 / pgs. 1861-1862:
"There were those who envied Paul's reputation in the churches, and endeavoured to supplant and undermine him. However, there were others who were animated by Paul's sufferings to preach Christ the more vigorously. This made them the more bold to preach the word. How easy he was in the midst of all. It is God's perogative to judge of the principles men act upon; this is out of our line. Paul was so far from envying those who had liberty to preach the gospel that he rejoiced in the preaching of it even by those who do it in pretence, and not in truth."
I agree with those who had commented that the passage was speaking primarily of one's inner motivations. It certainly doesn't seem to be an argument over doctrinal issues, but over the inner motivations and heart condition of those doing the preaching.