What present-day monarchs descend from Rodrigo de Borgia, a.k.a., Pope Alexander VI?

The (probably incomplete) data from Wikidata shows 12105 descendants of Alexander VI, among them 53 have "ocupation" "sovereign" or a subclass or it and 5 of those 53 monarchs are still alive (no date of death in Wikidata): the incumbent prince of Liechtenstein Hans Adam II, the incumbent king of the Belgians Philip I and his father the former king Albert II, and the incumbent king of Spain Philip VI and his father the former king Juan Carlos I.

Therefore, the answer is that if Wikidata is right, there are three present day monarchs descendants from pope Alexander VI: the monarchs of Liechtenstein, Belgium and Spain. The monarchs of several extinct monarchies (like those of Portugal and Italy) also descended from the pope Borgia.

PART ONE: General discussion.

Here is the simplest way I know to research such questions:

Here is a link to the surnames list at the Genealogics website.

http://www.genealogics.org/surnames.php1

So one would select the latter B:

http://www.genealogics.org/surnames-oneletter.php?firstchar=B2

And then select the surname Borgia:

http://www.genealogics.org/search.php?mylastname=BORGIA&lnqualify=equals&mybool=AND3

And then select the Borgia person you want to look at - presumably Lucrezia Borgia born 1480, since you seem to state that she was Aexander VI's only child to have descendants among modern royalty:

http://www.genealogics.org/getperson.php?personID=I00002961&tree=LEO1

Then link on the tab to show her descendants. You can choose how many generations to show, up to eight (the person and 7 generations of descendants) or even select show all descendants - which should be a very large file.

In the 7th generation Eleonore Gonzaga (1630-1686) should be a good lead to follow. She married Emperor Ferdinand III and their great grandson Emperor Francis I married Maria Theresa and was the ancestor of the House of Habsburg-Lorraine. If you can find any members of the House of Habsurg-Lorraine who married into Protestant families then you can find Protestant descendants of Lucrezia Borgia.

In the 6th generation Anne Gonzaga (1616-1684) married a protestant, Edward, Count Palatine of Simmern (1625-1663), who converted to Catholicism. Thus their Catholic descendants were ineligible to inherit the English throne.

So this is my suggestion for researching whether there are any Protestant descendants of Rodrigo Borgia. I hope it helps you find out.

Wait, I just noticed that your question mentions some Protestant dynasties you think are descended from Rodrigo Borgia, specifying Hess, Mecklenburg, and the Prussian Hohenzollerns.

King Christian IX of Denmark, called "the Father-in-Law of Europe" because of all the royal marriages made by his children, married Louise of Hesse-Kassel (1817-1898) If Louise of Hesse-Cassel was descended from Rodrigo Borgia then all the Protestant and eastern orthodox descendants of King Christian IX also are.

Added 03-16-2019. The original question mentions three protestant Dynasties, the Hessen, Mecklenburg, and Hohenzollern dynasties, that were descended from Rodrigo Borgia. However, those dynasties had many different branches.

Adolphus Fredrick II (1658-1708), the first Duke of Mecklenburg-Strelitz, doesn't seem to be descended from Rodrigo Borgia. https://en.wikipedia.org/wiki/Adolphus_Frederick_II,_Duke_of_Mecklenburg-Strelitz2

Frederick II (1717-1785), Duke of Mecklenburg-Schwerin, doesn't seem to be descended from Rodrigo Borgia. https://en.wikipedia.org/wiki/Frederick_II,_Duke_of_Mecklenburg-Schwerin4

Charles I, Landgrave of Hesse-Kassel (1654-1730) seems to have had no descent from Rodrigo Borgia. https://en.wikipedia.org/wiki/Charles_I,_Landgrave_of_Hesse-Kassel#Ancestry3

Ernest Louis, Landgrave of Hesse-Darmstadt (1667-1739) seems to have had no descent from Rodrigo Borgia.https://en.wikipedia.org/wiki/Ernest_Louis,_Landgrave_of_Hesse-Darmstadt5

King Fredrick I of Prussia (1657-1713), of the House of Hohenzollern, doesn't seem to have had any descent from Rodrigo Borgia. https://en.wikipedia.org/wiki/Frederick_I_of_Prussia#Ancestry6

Christian-Ernest Margrave of Brandenburg-Bayreuth of the House of Hohenzollern (1644-1712), doesn't seem to have had any descent from Rodrigo Borgia. https://en.wikipedia.org/wiki/Christian_Ernst,_Margrave_of_Brandenburg-Bayreuth7

William Frederick, Margrave of Brandenburg-Ansbach of the House of Hohenzollern (1686-1723), doesn'tseem to have any descent from Rodrigo Borgia. https://en.wikipedia.org/wiki/William_Frederick,_Margrave_of_Brandenburg-Ansbach8

The branches of Hohenzollern-Hechingen and Hohenzollern-Sigmaringen are Roman Catholic and not protestant.

If any later members of the houses of Mecklenburg, Hesse, and Hohenzollern were descended from Rodrigo Borgia, it would have to be through marriages with members of other dynasties.

PART TWO: List of marriages of Borgia Descendants with Protestants.

As was said above:

King Christian IX of Denmark, called "the Father-in-Law of Europe" because of all the royal marriages made by his children, married Louise of Hesse-Kassel (1817-1898) If Louise of Hesse-Cassel was descended from Rodrigo Borgia then all the Protestant and eastern orthodox descendants of King Christian IX also are.

Louise of Hesse-Kassel was the great great great granddaughter of Charles I of Hesse-Cassel who doesn't seem to have been descended from Rodrigo Borgia. So if she had any descent from Rodrigo Borgia to transmit to her Protestant descendants it would have come from one of the wives in her ancestry.

https://en.wikipedia.org/wiki/Louise_of_Hesse-Kassel

As I wrote above:

In the 7th generation Eleonore Gonzaga (1630-1686) should be a good lead to follow. She married Emperor Ferdinand III and their great grandson Emperor Francis I married Maria Theresa and was the ancestor of the House of Habsburg-Lorraine.

So I tried looking at the descendants in 8 generations of emperor Francis I and Empress Maria Theresa.

http://www.genealogics.org/descendtext.php?personID=I00000016&tree=LEO&display=block&generations=89

A 7th generation descendant, Marie of Orleans, married Prince Valdemar of Denmark (1858-1939), their daughter was a Catholic and their sons were Lutherans.

A descendant of Emperor Francis I in 6 generations, Leopoldine of Brazil, married Prince Ludwig of Saxe-Coburg & Gotha (1845-1907) and had many children.

A descendant in 6 generations, Archduchess Margaret Sophie, married Duke Albreacht of Wurttemburg (1865-1939), head of the House of Wurttemburg. Since different branches of the dynasty were Catholic or Protestant I forget whether this branch is Protestant or Catholic.

A descendant in 6 generations. Maria Louisa of Bourbon-Parma, married King Ferdinand of Bulgaria (1861-1948).

A descendant in 7 generations, Princess Maria de las Mercedes of Spain, married Prince Iraklij Bagration-Muchransky (1909-1977).

A descendant in 7 generations, Archduchess Illona, married George, Count of Carlow and heir of Mecklenburg-Strelitz (1921-1926).

A descendant in 7 generations, Clothilde, Princess Napoleon, married Sergei, Count de Witt (1891-1990).

A descendant in 7 generations, Mafalda, Princess of Savoy, married Prince Philip of Hesse (1896-1980).

Her sister Giovanna, Princess of Savoy, married Boris, King of Bulgaria (1894-1943).

A descendant in 6 generations, Antonia, Princess of Portugal, married Leopold, Prince of Hohenzollern 91835-1905), and their descendants include the Royal family of Roumania.

And there are probably some more examples.