The Israeli-Palestinian conflict is very complicated. At some risk let me try to add some perspective.
"Illegal" is a broad term, but most jurists agree that the Israeli settlers are acting in violation of the Fourth Geneva Convention sections of occupation. While the United States (and others) are not signatories to the ICC, they are signatories to the Fourth Geneva Convention.
If anyone wants to really discuss the legality of the Israeli settlements I recommend you read those sections before you start. That statute is the foundation of the issue.
The American position has been nuanced. At various times they have stated those actions are illegal, while at other times they have refrained from using that term and referred to them as "illegitimate, provocative and obstacles to peace." The United States' reasoning (as I understand it) is that they prefer a diplomatic solution to the conflict and believe that a simple position of "illegal" or "legal" reduces room for diplomatic efforts. For what it's worth I think Reagan etc were quite right about that.
Trump has leaned away from the traditional "illegitimate" approach more toward's Israel's position but has not abandoned it entirely. He too is discovering that on various issues Israel can be a difficult ally to contain.
One of the problems that Israel faces in reaching any kind of agreement with the Palestinian people is that they don't have a singular legitimate body you can negotiate with to reach an agreement. At least with Israel you know who you have to negotiate with.
The second problem that Israel (and the world) faces in achieving a solution to the Palestinian issue is that no effective Palestinian group has recognized Israel's right to exist as a Jewish state.
Until there is a singular representative group of the Palestinian people that recognizes the right of Israel to exist as a Jewish state, it seems unlikely any significant diplomatic progress can be made.
Not to pick a fight, but after examining the claims of the so called "Palestinians", I find most of them to be baseless. If we go back just 150-200 years, most of these so called Palestinians came from Jordan (ethnic Heshemites), or Egypt. They never owned land in the area now claimed as a Jewish State.
To start off, the Jews have maintained a continuous presence throughout the area, including North Africa, Arabia, and Persia for nearly 3,500 years. However, this presence does not mean ownership, of land or anything else, for Israelites or Arabs.
When photography became widespread, it shocked most Americans to learn that the "Holy Land" was so sparsely populated. Samuel Clements, known to the World as Mark Twain described much of the countryside as being devoid of human presence.
Abroad, Mark Twain, 1867.
Excerpt from The Innocents Abroad, Mark Twain, 1867.

There is not a solitary village throughout its whole extent [valley of Jezreel] — not for 30 miles in either direction… One may ride ten miles hereabouts and not see ten human beings. … For the sort of solitude to make one dreary, come to Galilee … Nazareth is forlorn … Jericho lies a moldering ruin … Bethlehem and Bethany, in their poverty and humiliation… untenanted by any living creature… A desolate country whose soil is rich enough, but is given over wholly to weeds … a silent, mournful expanse … a desolation … We never saw a human being on the whole route … Hardly a tree or shrub anywhere. Even the olive tree and the cactus, those fast friends of a worthless soil had almost deserted the country … Of all the lands there are for dismal scenery Palestine must be the prince. The hills barren and dull, the valleys unsightly deserts [inhabited by] swarms of beggars with ghastly sores and malformations. Palestine sits in sackcloth and ashes … desolate and unlovely …
Hardly the bustling Palestinian population center they would have us believe.
Even worse for the Arab argument is the fact that most were Bedouins who were perpetual wanderers, and therefore owned no land. Many were actually of Jordanian birth, and possessed Jordanian papers.
The Jews on the other hand, purchased the land from it's Ottoman Turk owners, at exorbitant prices. The Jews actually hold title to much of the land. Even the Grand Mufti of Jerusalem, Haj Amin Al Husseini was compelled to admit this to the British Peel Commission in 1937. Al Husseini and his family were on lists of individuals who had sold land to Jews, while at the same time organizing strikes and violent riots that killed dozens of Jews as soon as they moved onto the land.
This same Haj Amin Al Husseini spent most of WWII under the protection of Adolf Hitler.
Al Husseini eventually helped to form a Muslim SS Division within the German Army. Not so much to be used in combat against Russia or the Western Allies, but to round up and ship Jews in southern Europe and Arabia to the Death Camps.
In the picture below, Al Husseini tours the Trebbin Concentration Camp just south of Berlin.
In this photo dated 1943, Al Husseini meets with Heinrich Himmler. There can be absolutely no doubt that the entire leadership of Muslim "Palestine" knew the fate of the Jews they were persecuting, and shipping to the Death Camps.
The entire story of how the Jews stole the land in 1948, and therefore created Palestinian hatred is a fabrication.
Back to the actual question of who owns the land, and where the so called "Palestinians" are actually from.
The Heshemites and Egyptians who came to the area for work after the Jews established farms, did not own land, or count themselves as "Palestinians" as that was a pejorative term for Jews at the time.
You can't steal land from people who never owned it, or were citizens of other countries.
After the War of 1948, Arab leaders expelled Jewish Communities all over the Arab World, often at gunpoint, and into the new nation of israel. Funny how no Arab source bothers to mention the expulsion and widespread Pogroms against Jews in Muslim Countries.
Arabs within Israel were forced out, often returning to the lands their parents had come from prior to 1900. The Arabs call this the NAQBA, or disaster. Arab Leaders, including Al Husseini, told Muslim residents of what became Israel to leave, as it would make it easier to kill the Jews if they were all in one place.
Hard to claim your land was stolen when your Leadership tells you to leave so your neighbors will be easier to kill. Then when you lose, those same neighbors don't let you back in?
Bottom line?
I don't feel one ounce of pity for the Arab population in that region, nor do I believe they have much of a legal leg to stand on as far as land ownership. They sowed the wind....