There are many rumors saying that Donald Trump would like to rerun for president in 2024. Many Republicans argue that Donald Trump has destroyed the image of the GOP and after republicans blamed Donald Trump for the US Capitol mob. Since these circumstances and Negativity towards Trump, could the Republican Party refuse to allow Trump to run on their platform and probably a nomination?
Assuming that Trump has not been barred from office (as by an impeachment and conviction, or a conviction for a crime which imposes a ban on holding office) then the party as an organization cannot prevent him from filing as a candidate. It can decline to endorse or support him. But should he win sufficient primary elections, he would be the party nominee. The various court cases outlawing the so-called "white primary" in the 1st half of the 20th century drastically restricted the ability of a party to limit who might run under its banner. See Nixon v. Herndon, 273 U. S. 536 (1924), United States v. Classic, 313 U.S. 299 (1941), Smith v. Allwright, 321 U.S. 649 (1944) and the Wikipedia article about the Smith case. The court in Smith said:
exas is free to conduct her elections and limit her electorate as she may deem wise, save only as her action may be affected by the prohibitions of the United States Constitution or in conflict with powers delegated to and exercised by the National Government. The Fourteenth Amendment forbids a state from making or enforcing any law which abridges the privileges or immunities of citizens of the United States ...
It may now be taken as a postulate that the right to vote in such a primary for the nomination of candidates without discrimination by the State, like the right to vote in a general election, is a right secured by the Constitution.
Much the same logic would apply to the right to be a candidate in a primary, it5 is secured by the US Constitution.