It's really a question of whose appearance....
I understand there was a day when even the appearance of impropriety or conflict of interest was the gold standard for politicians. But, in truth, that merely meant the politicians made sure they kept their business dealings very private. LBJ made himself a rich man when he was out of office by buying a local broadcast company (KLBJ still operates a radio station and a TV station in Austin. In the days when nobody watched TV except on broadcast, and only on VHF, LBJ made sure any other TV station in Austin had to broadcast on UHF.). And he steered a lot of government contracts (which benefited people along the lower Colorado River, to be sure, as well as the entire City of Austin) to the company which became Brown & Root (and they returned the favor). Rick Perry has never worked for anything but the Texas government (or the National Guard) his entire adult life, yet he doesn't have to work now that he's unemployed. Oddly, no one ever called these benefits of public life the appearance of a conflict of interest (we got close when Perry issued a mandate that all school age female students in Texas take the vaccine Gardasil before enrolling in public schools. Merck was a major campaign contributor to Perry, and the Lege overrode is order as soon as possible; mostly because of the connection between teenage sex and the human pamplona virus, however, not because of Perry's ties to Merck.).
So it's a fluid standard that isn't yet being applied to Trump, possibly because the NYT (and others) don't imagine Trump has a snowball's chance in hell of winning the White House. Trump, however, has said he'll let his kids run his business, but he won't put it in a blind trust. He says he won't care about his business anymore, and since he's always consistent in his public statements we can trust him, right?
I don't know why no one takes him seriously, but is having a serious fit of the vapors over what Hillary Clinton's connection to a charitable foundation might mean. Except this concept of "appearance" pretty much died with Bill Clinton's impeachment, an impeachment he was was responsible for as the pedestrian is responsible for being in the crosswalk when the driver of the car refuses to slow down.
Republicans took the concept of "appearance" and responsibility for same to its logical conclusion in that impeachment; and to this day it is only applied to Democratic presidents. There was an "appearance" of conflict when the Bush Administration contracted with Halliburton to fight in Iraq but somehow it wasn't taken all that seriously. Maybe it's because the GOP always raises the issue, but the appearance in this case seems to be more troubling to the NYT and others, than any appearance of conflict by a GOP President (up to and including George H.W.'s ass saving pardon of everyone involved in Iran-Contra, before they could reveal how "out of the loop" the elder Bush wasn't). And frankly, after that, the American public pretty much took "appearance" of either conflict of interest or impropriety to be as out-dated a notion as hotel dicks making sure Mr. and Mrs. Jones were married to each other.
You can be sure, however, that the newspaper that gave us Whitewater and the subsequent non-scandals of the first Clinton administration would keep the "appearance of conflict" story in the news through the second Clinton administration. The NYT is already trying to tie Anthony Weiner's bizarre predilections to Bill Clinton's term in the White House. You can't make this stuff up.
Because, after all: both sides do it, donchaknow?