Should I embed color profile?

…the idea of and having to re-save and store twice as many files (one cmyk and one rgb) seems daunting (to me and my external hard drive). Not to mention I'd have to re-place all the images in InDesign depending on the file output.…Is there a specific way to set up my InDesign document so the photos' color profiles can switch automatically depending if I export it for print or digital?

By @Shelby30619457p4h8

The most current workflows already work that way: A single document, in an RGB color space that’s large enough to cover most online and print colors. When it’s time to deliver any specific kind of output from that (print, web…), a copy is created which is converted for that type of color output. Using an InDesign job as an example:

1. The original document and images are in Adobe RGB. 

2. When it’s time to hand off print files, a copy of the original is exported as PDF using a preset tuned to the specs required by the printing company (such as PDF X-1a or PDF X-4). They will run that through their equipment, which will convert it to the specific color values needed for their printing equipment.

3. When it’s time to hand off web files, again you go back to the original, and export copies tuned to the color specs and pixel dimensions for the web.

It used to be more common to edit originals in the final color space (such as CMYK), but that was common only back when print was the dominant medium. As the types of delivery media diversified and print became less common than RGB-based screen delivery, the workflow moved to the current model of keeping an original in a large RGB color space, and deriving color-optimized print and online web copies from that as needed.

For more details, you might want to read this article by industry veterans:

Why You Should Import RGB Images Into InDesign and Convert to CMYK On Export (CreativePro Magazine)

But the last word needs to be this: Whatever the “best practice” is, the right thing to do is always whatever is required by the company handling the job. If a job is being printed somewhere where they never changed the way they’ve done it for 30 years and so they still require you to send in files as CMYK, then that’s what you have to do (but make sure to convert using the exact CMYK profile they use). If a different and fully modernized printing company says to submit a job as PDF X-4, then for them, in InDesign you just run your job through that PDF export preset and hand that off.

For images, you can maintain full quality RGB originals in a folder, and when it’s time to hand off a set for a website or video or whatever, you can use the bulk export features in Adobe Bridge, Adobe Photoshop, or Adobe Lightroom Classic to convert copies of all of the images at once to the required color space.

Without a profile, the numbers mean nothing:

Always embed the profile. No exception!

The profile is what defines the numbers as actual colors. Without a profile, it's undefined and unpredictable.

As for print vs. web, the way you deal with this is to place RGB mages in your master InDesign file. Then you convert to the appropriate output when you export to pdf from that master InDesign file.

There are still applications that don't support color management, and then the profile is ignored. Without color management, there is no possible way to predict the outcome anyway.  You should try to avoid those situations, but if you can't, sRGB has the highest probability of being represented (roughly) correctly, in the highest number of possible scenarios.

Why do you save your images without profiles? No application will know how to display or convert them correctly because they cannot be color managed.

Start by setting up your color management with the correct profiles for print and online (the last sRGB).

I would save the Photoshop files as RGB, place them in an InDesign document destined for print and export 2 pdf versions, one with an online preset and one for print (talk to your print about the pdf settings).

Let color management do the work with a single source.