creative writing - How does one write from a minority culture? A question on cultural references

Christian culture is dominant. Thus, even without being Christian myself, I can recognise, understand and appreciate references that are within that culture, like the Pietà:

Sam sat propped against the stone, his head dropping sideways and his breathing heavy. In his lap lay Frodo’s head, drowned deep in sleep; upon his white forehead lay one of Sam’s brown hands, and the other lay softly upon his master’s breast. Peace was in both their faces. (J.R.R. Tolkien, The Lord of the Rings, book 4, chapter 8 - The Stairs of Cirith Ungol)

or carrying the Cross:

He unstepped the mast and furled the sail and tied it. Then he shouldered the mast and started to climb. It was then he knew the depth of his tiredness. He stopped for a moment and looked back and saw in the reflection from the street light the great tail of the fish standing up well behind the skiff's stern. He saw the white naked line of his backbone and the dark mass of the head with the projecting bill and all the nakedness between.
He started to climb again and at the top he fell and lay for some time with the mast across his shoulder. He tried to get up. But it was too difficult and he sat there with the mast on his shoulder and looked at the road. A cat passed on the far side going about its business and the old man watched it. Then he just watched the road.
Finally he put the mast down and stood up. He picked the mast up and put it on his shoulder and started up the road. He had to sit down five times before he reached his shack.
Inside the shack he leaned the mast against the wall. In the dark he found a water bottle and took a drink. Then he lay down on the bed. He pulled the blanket over his shoulders and then over his back and legs and he slept face down on the newspapers with his arms out straight and the palms of his hands up. (Ernest Hemingway The Old Man and the Sea)

Visiting museums, I have seen thousands of crucifixions, hundreds of pietàs and annunciations. I can recognise saints by their attributes. But this is not my culture.

Is there any way I can make similar references to my culture in the stories I write? (Doesn't really matter what my culture is - the question should be equally valid for any cultural minority.) I guess I cannot expect all references I make to be understood by all readers (one doesn't necessarily see the pietà in The Lord of the Rings when reading it for the first time either, and one definitely doesn't get all literary references in any given example of classic literature without some study) but at the very least I want to make sure I do not push people away by unfamiliar references.

(Question partially inspired by this answer to Cyn's question.)