I have two fireplaces that are white painted brick, they were like that before we bought the home, and the outside of my house is white painted brick so it all goes. I actually really love the look of my painted brick... I have kind of an eclectic coastal thing going on.
However, I really like the color of your brick. It adds a nice texture to the room.
I will also tell you that one drawback of my painted brick is that it's hard to keep the top of the hearth looking clean in my family room. Everyone sits there, food and drink gets spilled on it... it just gets looking grimy and it doesn't clean up well so I end up slapping more white paint on periodically. No one sits on the hearth in my kitchen though and that hasn't been difficult to keep clean looking. So just some food for thought depending on how your room gets used. :)

Here's one of my fireplaces... and it's gas and we have used it once in the six years we've lived here. If you look close enough you can see marks and nasty "patina" on the hearth. LOL! The white paint just doesn't hide anything.
I still love my fireplaces... it's just something to consider is all.

Here's the one in my kitchen I took recently (to show how I'd blocked off the opening because we have a terrible draft from it otherwise) but you can see the top of the hearth isn't so bad like my other one... nobody ever uses this one as a place to sit, that's the difference.

Absolutely paint it!

Don't paint the fireplace. It is lovely. I have close to the same color brick fireplace with a raised hearth. I painted my bookcases also white. There was something not quite right and I knew it wasn't the fireplace. The fireplace did not tie in with the white bookshelves. My husband bought thin furniture grade unfinished wood sheets. He cut them to fit each shelf in the bookcase. I stained them a rich brown. That is what was needed. The fireplace by its self was lovely and the shelves themselves were lovely, it just didn't tie in together. The stained wood shelves in the white book cases is what was needed to tie both together.

Completely agree with functionthenlook. I have the same issue with my stone fireplace. It looks dingy next to white wall but with a complimentary color it looks terrific.

Another solution might be to line the backs with a softer color, maybe foam core or cover board with fabric or paint.

functionthenlook, if it’s not too much to ask, can you post a pic of your fireplace? I like your idea.

Thanks! I like the idea.