I'm using the custom proof setting in Photoshop for the Blurb ICC profile which is CMYK. Yet same color file inside of Indesign will look different. Help
You mean in Photoshop you are editing in RGB (sRGB?) and soft proofing through Blurb's custom CMYK profile, then placing the RGB file in ID (you're not converting to CMYK)? If so, are you also setting up ID's proof setup the same way—the Working RGB space matches Photoshop's (sRGB), and the Proof Setup matches also (Blurb CMYK)?
Keep in mind the Proof Setup/Proof Colors feature in both programs soft proof source color (the file's color mode and values) to a destination device without actually making the color conversion. So you could be soft proofing to a specific device, but sending out different color—i.e. you soft proof to a custom CMYK profile, but hen send out an unchanged PDF with a mix of RGB and CMYK objects.
And there's also the possibility that the profile isn't accurate. Just because they send it out doesn't mean they take the time to keep the printers calibrated. I recently had a job printed on an Indigo (not by Blurb) and went to the trouble to have sample prints made of the color critical pages so I could make sure I had my color right using the profile supplied. Several weeks later when they finally got around to sending the client a proof of the final book layout, the color wan't even close to the samples he approved.
Looking at Blurb's printing specs they recommend sending sRGB not CMYK:
They do offer a CMYK profile for soft proofing probably so users see RGB color in some CMYK gamut. I think most online printers do not allow CMYK to be output unchanged particularly if they offer uncoated printing—where unchecked total ink would be an obvious problem in an automated offset process.
Blurb offers one CMYK profile (looks like they've simply renamed Coated GRACoL) even though they print on a variety of coated and uncoated sheets, so even if you converted everything to CMYK using the provided profile, it is unlikely that those CMYK values would get printed—Coated GRACol would not work for Mohawk Superfine.
Since it's likely that all color will get converted on their end, providing the recommended sRGB and avoiding extra conversions is the best bet.