Does any real existent or genuine person end with parinibbana? Does modern Theravada accept that no real person ends with the break up of the body of a realized one? That the moment after the break up of the body of a realized one is the same as the moment before?

In SN 22.85 With Yamaka (sujato) and alternative translation Sariputta seems to rebut the notion that any substantial change happens during the break up of the body of a realized one:


  Now at that time a mendicant called Yamaka had the following harmful
  misconception: “As I understand the Buddha’s teaching, a mendicant who
  has ended the defilements is annihilated and destroyed when their body
  breaks up, and doesn’t exist after death.”
  
  Several mendicants heard about this. They went to Yamaka and exchanged
  greetings with him. When the greetings and polite conversation were
  over, they sat down to one side and said to him:
  
  “Is it really true, Reverend Yamaka, that you have such a harmful
  misconception: ‘As I understand the Buddha’s teaching, a mendicant who
  has ended the defilements is annihilated and destroyed when their body
  breaks up, and doesn’t exist after death.’” “Yes, reverends, that’s
  how I understand the Buddha’s teaching.”
  
  “Don’t say that, Yamaka! Don’t misrepresent the Buddha, for
  misrepresentation of the Buddha is not good. And the Buddha would not
  say that.” But even though admonished by those mendicants, Yamaka
  obstinately held on to that misconception and insisted on stating it.


After talking with Sariputta it seems Yamaka has a change of heart after this question by Sariputta:


  “What do you think, Yamaka? Do you regard the Realized One as one who
  is without form, feeling, perception, choices, and consciousness?”
  “No, reverend.” “In that case, Reverend Yamaka, since you don’t
  acknowledge the Realized One as a genuine fact in the present life, is
  it appropriate to declare: ‘As I understand the Buddha’s teaching, a
  mendicant who has ended the defilements is annihilated and destroyed
  when their body breaks up, and doesn’t exist after death.’?”


Here is the same portion in Venerable Bodhi's translation:


  “But, friend, when the Tathagata is not apprehended by you as real
  and actual here in this very life, is it fitting for you to declare:
  ‘As I understand the Dhamma taught by the Blessed One, a bhikkhu whose
  taints are destroyed is annihilated and perishes with the breakup of
  the body and does not exist after death’?”


So does this mean the break up of the body is just like any moment in this very life where moment to moment no person truly ends or changes because a real person doesn't truly exist in the first place?

EDIT:

I'm aware that orthodox Theravada tenet systems posit the selflessness of persons, but are either agnostic or outright reject the selflessness of phenomena. However, most pali canon suttas seem to stop at the coarse level of selflessness, but here Sariputta seems to be speaking about the subtler levels of the selflessness of persons if only in embryonic form. Is this true?

Also, if the body of a person is regarded as a real substantial thing in Theravada how about the consciousness of a person? Is that regarded as a real substantial thing?
I think you (the OP) have mistakenly assumed that the Pali Yamaka Sutta supports the Mahayana Madhyamika concept of emptiness that nothing is substantially real.

Actually, the Yamaka Sutta quote of the Bodhi translation indeed confirms emptiness, but it's the Theravada emptiness and not the Mahayana emptiness. And what is the Theravada emptiness? It's that all phenomena is empty of a self (see Suñña Sutta). Before parinibbana, there was no self (as in an eternal self or soul at the core of the Buddha's being) that has suddenly ceased to exist after parinibbana.

However, the Pali suttas do not explicitly support the Mahayana Madhyamika concept of emptiness. The  Buddha's body was considered to be real but not constant or permanent. It is subject to change, arising and ceasing. But that does not mean that it's not real in Theravada.

To prove this, I'll quote Itivuttaka 44:


  This was said by the Blessed One, said by the Arahant, so I have
  heard: "Monks, there are these two forms of the Unbinding property.
  Which two? The Unbinding property with fuel remaining, &amp; the Unbinding
  property with no fuel remaining.
  
  And what is the Unbinding property with fuel remaining? There is the
  case where a monk is an arahant whose fermentations have ended, who
  has reached fulfillment, finished the task, laid down the burden,
  attained the true goal, ended the fetter of becoming, and is released
  through right gnosis. His five sense faculties still remain and, owing
  to their being intact, he is cognizant of the agreeable &amp; the
  disagreeable, and is sensitive to pleasure &amp; pain. His ending of
  passion, aversion, &amp; delusion is termed the Unbinding property with
  fuel remaining. (Note1)
  
  And what is the Unbinding property with no fuel remaining? There is
  the case where a monk is an arahant whose fermentations have ended,
  who has reached fulfillment, finished the task, laid down the burden,
  attained the true goal, ended the fetter of becoming, and is released
  through right gnosis. For him, all that is sensed, being unrelished,
  will grow cold right here. This is termed the Unbinding property with
  no fuel remaining." (Note2)
  
  Note1 and Note2 by Thanissaro Bhikkhu:
  With fuel remaining
  (sa-upadisesa) and with no fuel remaining (anupadisesa): The analogy
  here is to a fire. In the first case, the flames are out, but the
  embers are still glowing. In the second, the fire is so thoroughly out
  that the embers have grown cold. The "fuel" here is the five
  aggregates. While the arahant is still alive,
  he/she still experiences the five aggregates, but they do not burn
  with the fires of passion, aversion, or delusion. When the arahant
  passes away, there is no longer any experience of aggregates here or
  anywhere else.


Next, to answer the question:


  OP: So does this mean death is just like any moment in this very life where moment to moment nothing truly ends or changes because it
  doesn't truly exist in the first place?


Before and after the Buddha's final passing, all phenomena is empty of a self. The Buddha's five aggregates existed and was subject to change, arising and passing. Nibbana existed and does not change, arise or pass away. But the self (in the sense of an eternal self or soul at the core of our being) never existed at any time, in all phenomena, including the five aggregates and Nibbana. This is the interpretation according to Theravada.

Your interpretation appears to be different and based upon the concept of Mahayana emptiness.