Julie sings "Can't Help Lovin' Dat Man" as an attempt to explain why she continues to love Steve.
In spite of his tendency to leave home without giving any reason and to return after indefinite periods of time, often late at night, she still adores him. It doesn't matter to Julie if he can't hold a job because he's "lazy" or "slow." His lack of attention to their housing - "De chimney's smokin', De roof is leakin' in, But he don't seem to care" - still doesn't dissuade her from "lovin' dat man of mine."
The situations she describes in the song were not unique. The clue that it was surprising to hear Julie singing the song comes from Queenie's comment that she had never heard anyone but "colored folks" sing it. Julie, at that time in the movie, was considered by the crew of the Cotton Blossom and the public to be white. Later in the film it is revealed that she is, in fact, mulatto, having mixed race parents. For a white man, such as Steve, to be married to a woman of mixed race was against the law during the time period in which "Showboat" was set.