WASHINGTON — Former Gov. Jeb Bush of Florida challenged some long-held tenets of conservative tax policy on Wednesday by proposing to curtail valuable deductions that benefit businesses and the wealthy and eliminate a loophole that has benefited hedge fund and private equity managers for years.

That an establishment Republican candidate has embraced such changes not only highlights how income inequality has altered the tenor of the presidential debate for the party, but also indicates the ideological pull Donald J. Trump’s candidacy is having on the Republican field after he made similar proposals.

Mr. Bush’s proposals nevertheless drew a harsh rebuke from Democrats who are unhappy that he is seeking to lower taxes across all income brackets and slash the corporate tax rate. At the same time, conservative anti-tax activists were worried by his suggestion that “carried interest” — the profits fund managers receive from investing other people’s money — should be taxed at a higher rate, like ordinary income.

“No Republican should be for higher taxes on capital gains,” said Ryan Ellis, the tax policy director at Americans for Tax Reform, which opposes all tax increases. “This tax hike idea is supported by Barack Obama, Hillary Clinton, Bernie Sanders and Elizabeth Warren. The Democratic left deeply wishes to tax all capital gains as ordinary income.”