I don't know how you can claim a deadline that was achieved was not realistic.
Full stack testing was not cutting corners. After ground testing it was deemed that incremental testing would not be beneficial. Doing tasks in parallel instead of in series can introduce project risks, but that's not the same thing as cutting corners, which is where something necessary is not done at all.
No, JFK consulted extensively with the engineers beforehand. The end of the decade timeframe first came from a NASA study published February 7, 1961. Kennedy's budget had actually rejected the initial proposal from Webb to fund the moon program for an end of the decade moon mission just a few weeks prior to Gagarin's flight. A new proposal was put together and presented May 8, 1961 for Johnson by James Webb, Abe Hyatt, and Robert Seaman which pushed for a moon landing by end of decade. Von Braun was even more aggressive, telling Kennedy that it could be done by 1968.
I am not a supermodel, I don't have the looks for it. But for everyone who has become a supermodel, it was most certainly realistic that they could become supermodels. If you have what it takes to accomplish a task, accomplishing the task is realistic. That's what the term realistic means.
Full stack testing was testing the entire rocket at the same time instead of using dummy stages to test parts of the rocket separately. There was opposition to it because if the rocket failed it might be difficult to diagnose why exactly it failed, which would slow the project down in the long run. Based on the ground testing and advances in instrumentation, the risk of a project delay from a failure was considered acceptable. It still took multiple launches to man rate the rockets. There's a reason the first manned launch of the Saturn V was Apollo 8.
Would you have gone up on that first manned Saturn launch? Not me. Recall how the space shuttle was safe, until it blew up. And then it was safe again, and broke up on reentry.
Everyone on the first manned Saturn test died. Do you know why people got into the second manned test? It was not that they knew with certainty it would be safe, but because they thought it was realistic that they could accomplish their goal.
People die in car accidents every day, that does not make my plan to drive to work tomorrow unrealistic.
Spend $257 billion dollars on powerball tickets and yeah, winning the powerball is quite realistic. Indeed you have better than a 95% chance of winning at least 300 times.