Top Republicans said Sunday that Donald Trump has changed the political playbook to such an extent that voters may not care that much about issues like his taxes or other episodes from his past.

“Donald Trump represents such a massive change to how things are done in Washington that people don’t look at…whether or not he releases his taxes or what this story was of 30 years ago,” Republican National Committee Chairman Reince Priebus told ABC on Sunday, referring to a Washington Post report that decades ago Mr. Trump masqueraded...