Does the Xbox One Afterglow controller use the same conductive rubber button contacts as the regular Xbox One controller?

Would a Xbone replacement part fit?

Looks like the answer is no.

As you can see in this picture, this are the rubber domes for the Xbox One/One S controllers:

According to the picture that you sent, the "pad" doesn't have the Guide button on the same piece and the separation between the Back/Start buttons is diferent making it incompatible:

I finally got my regular XBOX One spare rubber dome and was able to repair my controller.

Here is a comparison of the old (Afterglow) and new (XBOX One) rubber domes:

As you can see, the XBOX button rubber dome is attached to the main rubber dome and the rubber is generally larger around the actual conducting button part. What I did not photograph are the small rims on the other side of the gray rubber dome part. The black rubber dome is completely flat on the other side.

Below you can see that the dome does not fit very well.

These are the steps I did to make it fit:

• Cut away XBOX button part (has single part in Afterglow controller)
• Noticed that select/menu button do not sit very well, so I removed that part completely. Cut the original buttons off the black rubber dome and used those.
• (Not shown) remove the small rim on the other side of the gray rubber dome that made alignment very hard.
• Removed some excess material on the top left of the gray rubber part to fit the case.

In the end, all the buttons work again. I did have to reopen the case once because the rubber dome got misaligned (the registration hole is larger than the original). The button action is not as good as it was, but way better than before with the worn out rubber dome. It took me like 30 minutes to fix it.