Well, there were a few reasons he likely allowed the hijackers to land.

One of the easiest to point to is that he was not exactly the most stable of human beings. Some believe Idi Amin was a cannibal, famous for eating his enemies. He gave himself long, elaborate titles that made little sense, and claimed he was King of Scotland to boot. He was, quite simply, eccentric if we're being polite and unhinged if we're not. It's important to keep this in mind, because it colors some of our understanding of his decisionmaking. It was sometimes rational, but we should also be aware that sometimes he was not rational at all, by most standards.

One other reason I've read in passing (mentioned by Benny Morris in Righteous Victims) is that he was "probably bribed". I think that's probably wrong, and I've seen no information on it, but I know Morris is pretty good typically, so it's worth noting in passing here.

Another reason is simply that Idi Amin was himself quite antisemitic, and hated Israel too. When it came to Israel, he'd actually once been an ally, happily accepting Israel's surplus military materials and civilian projects. In fact, an Israeli company helped improve the Entebbe Airport, building a modern terminal before the hijacking. Israel had trained some of his troops in the 1960s, sent agricultural experts and crops, etc. This aid (from before Amin's rule) continued despite the fact that Amin had seized power in 1971 in a coup, but when he began to ban political activity, crack down, and asked for ever-more aid in fighting Kenya and Tanzania, Israel began to stop helping him. Uganda owed Israel plenty of money for the sales it had made of weapons and construction projects, but Amin asked Israel to basically write off the debt, which it refused to do. Instead, Amin basically flipped Uganda's allegiances, asked Libya and Saudi Arabia for help, and took their aid on the condition that he effectively end relations with Israel and expel Israelis from Uganda.

He proceeded to become a devout Muslim, expelled Gujarati Indians (who he blamed for economic problems) while referring to them as "brown Jews", expropriated their property, and then dismissed any Asians in the civil service and replaced them with Palestinians. Then he decided Jews as a whole were unwelcome, and outlawed Jewish practice among the black Jewish community in Uganda, and he closed all synagogues. His conversion was so complete that he applauded the murder of Israeli athletes in Munich at the Olympics in 1972, and said it was great that it happened in Germany because that was where the Holocaust was.

So basically, he hated Israel, hated Jews, and had shown as much for at least 4 years before the hijacking. So it wasn't just sympathy to the Palestinian cause, though that's where he started his conversion. It appears he genuinely believed Jews were "not a people who work for humanity", in his words about "Israelis" (which is how he referred to those killed in the Holocaust, showing he had no distinction between Israelis and Jews). He was, as I said, likely quite unhinged already. When he greeted the hostages, he apparently was shouting "Shalom, shalom", but when a hostage asked him a question and called him "Mr. President" (his title), he became enraged and demanded to be addressed as "His Excellency Field Marshal Doctor Idi Amin Dada". Amin told the hostages that he was there because he knew they were innocent but hated Israel and Zionism. Throughout the experience, he repeatedly told them he was working for their release and acting as a "mediator". But these claims were not exactly right, as you should expect given the other information above. Instead, they reflected Amin's unhinged tendencies. One former cabinet member of his, for example, called him "nearly illiterate" and "violently unpredictable", and also "jovial and generous" when he wanted things.

Amin often told a story that he had a dream where his mother told him never to harm Jews. But he was, as I mentioned, unpredictable. The Israelis knew this well, and knew him well. One IDF member, during the hostage crisis discussions, recalled that he had been given a rifle (Amin actually did parachute training in Israel long before, but never earned the Israeli paratrooper wings he was fond of wearing because he never jumped), and promptly fired it at a courtyard full of innocent and unarmed people. One Israeli leader, noting the dream, also said that the hostages should be safe...as long as Amin didn't have another dream. The Israeli determinations that he wouldn't harm the hostages or interfere with a rescue attempt shifted as they learned more about the situation. The more they engaged in discussions with Amin, the clearer his duplicitousness became, as did his cooperation. While they initially believed he wouldn't interfere with rescue or protect the terrorists, he started making threats that any escape attempt would be met with the use of explosives that supposedly surrounded the terminal, killing them all. He also stated multiple times that the hostages would all die if Israel kept up its "Zionist activities". The hostages, too, became quite distrustful of him and his "generosity" over time, believing he had been cooperating all along, not mediating as he claimed.

So there was likely a mix of antisemitism, hating Israel, general unpredictability, and the like that motivated him. We may never really know exactly, because he was all over the place depending on who he spoke to, and those who are as unstable as he appeared don't always explain their thoughts, nor can we easily rely on them.