Is calling a white person "white bread" considered racist in everyday conversation?
"whitebread" is a wry or gently mocking expression originating in the African American communities of the United States which is most often used to describe a "white" person the user is on friendly terms with and the expression is not intended to offend or insult. "wry" adjective: 1. using or expressing dry, especially mocking, humor. synonyms: ironic, sardonic, satirical, mocking. see, google.com "wry" Link
A slightly more common but equivalent expression would be to refer to a "white" person as "Opie", as in Opie Taylor from Andy Griffith fame.
Belonging to the class of bland, clean-cut, middle-of-the-road suburbanite breeders. The Cleavers from the old TV show "Leave It To Beaver" are a familiar archetype of whitebread culture. see, The Urban Dictionary “white bread” Link
Most of the online dictionaries I've consulted don't seem to get the quality of "whitebread" I've included and refer to only the bland, insipid qualities which really connote to "lack of soul". But, in my personal experience, this is one of those, admittedly rare, occasions when the dictionary definitions are missing the more subtle nuances of the term - reporting as outsiders looking in - that said, "location, location, location!"
My understanding is that it is of American origin, and has to do with the mundane and uninteresting lifestyle which may be perceived of the white middle-class.
white bread
2. bland; conventional.
Random House Unabridged Dictionarywhite bread
North American
informal
Blandly conventional in a way that is regarded as characteristic of the white middle classes.
Oxford Living Dictionaries
Check out the example sentences to get a feel of how it can be used.
Here is an explanation of the meaning at The Phrase Finder.
Pertaining to the US white middle classes.
The Phrase Finder
Billy Joel's famous 1983 song Uptown Girl features the phrase, where he talks about an uptown girl living in her white-bread world, here are the lyrics: Link to lyrics in video
I'm gonna try for an uptown girl
She's been living in her white bread world
As long as anyone with hot blood can
And now she's looking for a downtown man
That's what I am
metrolyrics
It's interesting if you watch the video, a group of grease monkeys singing about a girl in her white-bread world who are working in what definitely looks like a rough part of the neighbourhood. You can obviously get the meaning intended by white bread here, though let's not forget this was 1983.
Here are two excerpts from an article from Huffington Post titled "How White Bread Became White Trash"
In truth, though, the pejorative “white bread” had earlier antecedents. In the diverse ranks of 1960s counterculture activism, the phrase had already come to signify everything bland, homogenous, suburban, chemical, and corporate—everything that the counterculture hoped to upend.
But, by the early 1980s, another usage had emerged. In this case, “white bread” signified almost the opposite: not dull affluent suburbia, but white trash. “White bread,” like broken-down trailers, came to denote poverty of a white and rural kind—the world described by residents of TV’s South Park as “a quiet, little, white-bread, Podunk, white trash, redneck corner of the U.S.A.” Huffington Post article
Also, you can look through this short discussion among users at The Phrase Finder giving their understanding of the meaning of white bread.
Thus "white bread" describes the bourgeoisie not only because its members are racially white but also because they subsist on highly processed commercial foods.
Phrase Finder discussion
NB: This is just the opinion of some internet user.
It's hard to tell whether today its primary meaning is related to white middle-class lifestyle, dull lifestyle, or as the Huffington Post article put it, to denote "white trash". There's no doubt that it can be used in a primarily racial way, as seen in your original quote. This can be said in light-hearted playfulness or as a hateful slur, depending on context.