Putting No Obstacles Before the Gospel Conference

In 2 Co 6:3-10, Paul tells the believers in Corinth:

3 We put no obstacle in anyone’s way, so that no fault may be found with our ministry, 4 but as servants of God we commend ourselves in every way: by great endurance, in afflictions, hardships, calamities, 5 beatings, imprisonments, riots, labors, sleepless nights, hunger; 6 by purity, knowledge, patience, kindness, the Holy Spirit, genuine love; 7 by truthful speech, and the power of God; with the weapons of righteousness for the right hand and for the left; 8 through honor and dishonor, through slander and praise. We are treated as impostors, and yet are true; 9 as unknown, and yet well known; as dying, and behold, we live; as punished, and yet not killed; 10 as sorrowful, yet always rejoicing; as poor, yet making many rich; as having nothing, yet possessing everything. (ESV)

In 1 Co 9:12, he makes the same point specifically in reference to his choice not exercise the right he had to financial support:

12…Nevertheless, we have not made use of this right [to receive support], but we endure anything rather than put an obstacle in the way of the gospel of Christ. (ESV)

As passages like these indicate, a commitment to no put obstacles in the way of the gospel was a central feature Paul’s “way of life,” which he taught “everywhere, in every church’ (1 Co 4:16-17). What does it mean for something to function as a “hindrance” or “obstacle” to gospel? What are some of main “hindrances to the gospel” identified in the New Testament, and why are they identified as such? In Paul’s mind, the pattern of life he taught and modeled was of such great priority, that he could simply encourage churches to look for those who live “according to the pattern/example that you have in us” (Php 3:17). What is this “pattern” to which our conduct is expected to conform, and what does it look like, in practical terms, to live according it? What message does such a pattern/way of life assume?