Operating under those assumptions, this would be a First Amendment violation under controlling law in D.C.
The starting point is Sherrill v. Knight, 569 F.2d 124 (D.C. Cir. 1977), which held that "denial of a pass potentially infringes upon first amendment guarantees." In that case, the Nixon White House refused to issue a press pass to a reporter for a liberal magazine, but refused to explain why beyond citing "reasons of security." The D.C. Circuit said that if the White House intended to open itself to the press, it needed to do so in ways that did not offend the First Amendment.
White House press facilities having been made publicly available as a source of information for newsmen, the protection afforded newsgathering under the first amendment guarantee of freedom of the press requires that this access not be denied arbitrarily or for less than compelling reasons. Not only newsmen and the publications for which they write, but also the public at large have an interest protected by the first amendment in assuring that restrictions on newsgathering be no more arduous than necessary, and that individual newsmen not be arbitrarily excluded from sources of information.
Given these important first amendment rights implicated by refusal to grant White House press passes to bona fide Washington journalists, such refusal must be based on a compelling governmental interest. Clearly, protection of the President is a compelling, “even an overwhelming,” interest... However, this standard for denial of a press pass has never been formally articulated or published. Merely informing individual rejected applicants that rejection was for “reasons of security” does not inform the public or other potential applicants of the basis for exclusion of journalists from White House press facilities. Moreover, we think that the phrase “reasons of security” is unnecessarily vague and subject to ambiguous interpretation.
Therefore, we are of the opinion that appellants must publish or otherwise make publicly known the actual standard employed in determining whether an otherwise eligible journalist will obtain a White House press pass.
Sherrill v. Knight, 569 F.2d 124, 129–30 (D.C. Cir. 1977).
In a nutshell, Sherrill is saying that when the government is granting press credentials to some and denying them to others, First Amendment principles require it to meet basic due-process requirements of notice and an opportunity to be heard. Therefore, those denied with an explanation for the denial and an opportunity to contest that denial.
In this case, it's not clear whether the White House has provided Acosta with a hearing and notice at all, which would itself be a violation if that situation continues for too long. But even if it does, the White House could not use the procedure to punish Acosta for exercising the First Amendment principles that the procedure is designed to protect.
If the opposite were true, i.e., Acosta "laid hands" on the intern, I'd guess that that would be enough to revoke his credentials, assuming the White House went through the appropriate procedure. Sherrill explicitly recognizes protecting the President and his family as a valid basis for denying access, and I assume the courts would extend that protection to White House staff, especially if the White House were to argue that an assault on staff suggests that the person can't be trusted around the president himself.