Yes. The commissioner of the IRS is appointed by the President (current one appointed by Trump) and can be dismissed at any time without cause. So if you want to continue in that role, you will do what the President wishes. You can always resign if you find the instructions not to your liking, of course.

Richard Nixon demanded that the IRS investigate his enemies, but the IRS commissioner at the time refused to do so and eventually testified against Nixon on this issue.

The IRS is a part of the Dept. of Treasury, which is run by Steven Mnuchin, a member of Donald Trump's cabinet.

No. That won't stop accusations of influence however. Each side believes that when the other side is in the White House they use the IRS to go after political enemies. Republicans particularly were very loud in accusing Clinton and Obama of using the IRS to go after people and groups. For example:

https://en.wikipedia.org/wiki/IRS_targeting_controversy