After trying to build bridges for a decade I sadly conclude that, There is space for black faces, and working class accents, but it's a tight space that produces Conformity, Invisibility & Stagnation. There may be some exceptions, but in general this is what myself and my friends have experienced:
Invisibility
Church groups sometimes give a minority a certain role where they appear visible on Sunday's and in photos, whilst not being given a proper voice to influence - thus invisible whilst visible.
Conformity
The minorities that manage to stay a long time within the group tend to have learned how to hold their tongue a lot. How much they are promoted and encouraged in ministry often depends on how much they have conformed to the cultural norms. The result, being that the majority culture is perpetuated whilst seemingly being validated with a small number of minority faces.
Stagnation
I think it may be that Cons Evanagelicalism has felt for a long time that it has arrived. So when minorities try to join, they are expected to continue in the same way as the higher-ups. There is already a perfected DNA that needs to be injected into the minorities that come on board. Some of this is explicit, some implicit. Some leaders will be aware of the explicit stuff, and even make public comments about how they need to change, whilst being unaware of so much implicit stuff. We end up with a movement that is far behind the multicultural state of our country. We end up with praxis that misses out too many issues people are dealing with. We end up with blindspots that never get exposed, sins that are never confessed and repented of.
For those discouraged at experiencing these things, I'd like to encourage you that you're free, and don't belong to the majority culture (1 Cor 9:19), and one day, it won't be like this, God's end game will succeed (Rev 7:9)!
UPDATE: Due to the large response this post received, here is a follow up
Ways we Make Minorities Invisible