In the Supreme Court of the United States, the Justices typically recuse themselves from participating in cases in which they have financial interests.–Wikipedia
I am not aware of an instance when a Justice chose to recuse due to nomination by a certain President.
Supreme Court Justices, once appointed to life terms, are supposed to be immune to improper influence. This assumption is false if Justices do act in the interest of the President who nominated them or their political party. Could a Justice nominated by President Trump rule on a case in which Trump is a defendant? The answer may well be yes. It would be up to the Justice to decide. In the Nixon tapes case, Chief Justice Warren Burger and Justice Harry Blackmun, both nominated by Richard Nixon, participated.
https://constitutioncenter.org/blog/when-do-supreme-court-justices-recuse-themselves-from-cases
When Justices Recuse, and When they Refuse
https://constitutioncenter.org/blog/anniversary-of-united-states-v-nixon/
New NY 23rd 
Justices almost never recuse themselves. Even when they have direct financial or family connections to a case. Example?
In 2000 the Bush v Gore case was decided to determine whether the state of Florida had the right to recount the votes in an extremely close election. According to FL state law they had to do so. According to the SCOTUS (5-4), that state law was not upheld. The 5 “states rights” Republicans on the court voted against states rights. They stopped FL form recounting the votes.
Clarence Thomas’s wife was working for the Bush transition and soliciting resumes for future jobs in the administration. So Thomas had a direct conflict of interest.
Eugene Scalia and John Scalia (sons of the justice) both worked for law firms hired by the Bush family and campaigns. Another direct conflict of interest.
On election night when early returns looked like a Gore victory, Sanda Day O’Connor became angry and said to guests at a party “this is terrible”. She wanted to resign but only if a Republican was POTUS, according to her husband.
So, 3 of the 5 votes giving Bush the presidency had either family conflicts or were openly hostile and prejudiced against Gore. None of them recused.
LikeLiked by 1 person
The ABA article cited claims there were 180 recusals during the 2016 term, most by Justice Kagan. I agree it is easy enough to find instances where a Justice might have recused and didn’t.
LikeLike
Presidents hope Justices they appoint will act as they expect. Chief Justice Earl Warren, nominated by Ike, was an exception. He put his responsibilities ahead of politics.
LikeLike
One thing is sure–what Supreme Court nominees tell the Senate and the public is self-serving BS.
LikeLike