"Assuming the percentages referenced above are accurate,"
Which they are.
"what is the reason for the near constant proselytizing by LGBT advocates?"
There are still Christians who are supportive of the LGBTIQA+ community. But the reason why people become allies of the LGBTIQA+ community is for a sign of respect and the fact these people are human too.
"From the percentages listed, one could argue that LGBT already have the acceptance they claim they are denied."
They don't have their acceptance from everyone. There are still way too many heterosexual movies, too many cases of homophobia, and in many places conversion therapy is still legal.
"Maybe Americans are just tired of something they already accept being shoved in their faces nonstop."
Maybe the conservatives were never interested in being shown the truth because many of them are homophobes. Nobody is tired of the LGBTIQA+ community unless they are conservative.