When using Lightroom CC, with custom color profiles, and creating a public collection, which generates a public url, the photos are synced there, but without applying the correct color profiles.
Instead, Adobe Standard is applied in the web gallery.
Manually uploading the custom color profiles to Lightroom Online or Lightroom didn't help.
If I use Lightroom Online I can, in the develop section, select the correct custom color profile, which then updates the image. However, on the web gallery and in albums, it still leaves the Adobe Standard Color profile.
I haven't checked in a web gallery, but if you are changing and then simply checking in an album online that has been opened while you have made the change have you tried refreshing the browser? I tried that just now switching camera matching profiles on an image, and it worked.
I have been experiencing the same problem and this is the first time I've seen this issue discussed online. But it's actually gotten worse for me. It used to just apply a stock profile upon publishing the album to the web. Now it's not even keeping the applied profile consistent when I back out of the individual editor view. It even shows that the correct profile is selected, but the colors are wrong until I select a different profile and then reselect the original.
In Adobe Lightroom CC, you can copy selective edits. So, select a wrong color profile, copy ONLY the profile portion of that image (that has the wrong color profile) and paste the edit to the entire album. Allow Lightroom to sync. Double check the web album to make sure the incorrect profile was applied. Then do those exact same steps but with the correct color profile. The web album should be corrected. This worked for me. It's too bad it doens't just work normally out of the box...