Paris, Illinois
August 22, 2021
The Oxford English Dictionary describes “acrost” as “U.S. dial. and colloq.” (A dialectal usage is peculiar to a region, social class, etc.; a colloquial usage appears more often in speech than in writing.)
The Dictionary of American Regional English says the use of “acrost” as a preposition or an adverb appears “throughout US esp among speakers with less than coll educ.”
DARE‘s earliest citation for “acrost” as a preposition is from a 1759 document in the Essex Institute Historical Collections in Salem, Mass.: “Ye enemy fird at our men a Crost ye River.”
The first citation for the adverbial usage is from a 1779 entry in the journal of William McKendry in the Proceedings of the Massachusetts Historical Society: “The Lake … is … about 8 miles acrost.”
The regional dictionary describes “acrost” as a combination of “across” and the “excrescent t.” (The OED uses the term “inorganic” to describe the “t” in “acrost.”)
DARE says an “excrescent” sound is one with “no historical basis” that “occurs frequently” in “regional and social patterns.”
Neither DARE nor the OED mention anything about Christianity and crosses in their items on “acrost,” and we see no evidence to support that theory of yours.
We’re not phonologists, but one possibility is that people may sometimes confuse “across” with “crossed.”
Another is that the phrase “across the” may get elided into something sounding like “across tuh,” so that what’s being garbled is “the,” not “across.”