Are these sources reliable, meaning that this is true? Or are there other sources that impeach or contradict them? What, in fact, do the most reliable sources say about Babur's attitude in this regard?
In the memoirs Babur himself wrote, the Bāburnāma, there's indeed a lot of beheading.
Some examples (by no means an exhaustive list):
Husain Mirza ordered that all prisoners should be beheaded; this not here only but wherever he defeated a rebel son, he ordered the heads of all prisoners to be struck off. And why not? Right was with him.
Our men brought in many of their braves; we ordered the heads of all to be struck off.
While we were there, Khudai-birdi Tughchi, then newly favoured with beg's rank, fell on some of Tambal's raiders and brought in a few heads.
Another time Qasim Beg led his braves out through the Needle-makers' Gate, pursued the Auzbegs as far as Khwaja Kafsher, unhorsed some and returned with a few heads.
He cut off a few heads and sent to me.
they got up with him, beat his Auzbegs well, cut off and brought in a few heads.
a hundred or two were taken, some were brought in alive but of most, the heads only were brought.
All this before we reach, on the same page 302, these statements of Babur:
Those our men had brought in as prisoners were ordered to be beheaded and a pillar of their heads was set up in our camp.
Our men went straight up, broke into it and cut off a hundred or two of insolent Afghan heads. There also a pillar of heads was set up.
The edition of the Bāburnāma linked above has a note on this:
This barbarous custom has always prevailed amongst the Tartar conquerors of Asia (Erskine). For examples under Timur see Raverty's Notes p. 137.
There are more examples in pages 303, 441 and 474.
I don't know if Babur enjoyed using human skulls as Lego, but by the tone of his comments, certainly very upset he was not.