Can you remove a diagram from a provisional application when filing for a utility patent and not change the priority date?
In the US, it is permissible to remove information from the patent and still preserve the priority claim. Many nonprovisional applications will include a statement at the beginning that the provisional application is hereby incorporated by reference in its entirety into the present disclosure. So they're effectively saying "everything in the original provisional application should be considered a part of this application too" (or something along those lines--I don't remember the exact language). That's not a bad move, because if you omit something and later realize it's needed in order to overcome an examiner's rejection, then you can easily add it back in with no risk that you're adding new material. Moreover, you don't want a court to later say that your description fails to "enable" the invention when the diagram is omitted. Incorporating the provisional application by reference might help avoid that sort of issue.
The priority date applies to any material that is described in the original provisional application. If the nonprovisional application includes new material that wasn't in the provisional application, then that material doesn't receive the benefit of the earlier priority date.
Once the nonprovisional application publishes, I believe anyone can view the original provisional application in its entirety by going into the USPTO's PAIR system. For example, if you search for an application by number and put in 62/343525, you'll be able to click on the "Image File Wrapper" tab and then click on the links (specification, drawings, etc.) to see the various parts of the application.
There's a lot about this that I don't fully remember. The info above could be wrong. I'm not a patent attorney. As always, it's extremely important to contact an expert who practices patent law.
I am no expert, and this response is for informational purposes only and not for the purpose of providing legal advice. You should contact your attorney or legal expert to obtain advice with respect to any particular issue or problem. Laws can differ dramatically from country to country, state to state, and technology field to technology field.