But why burden the child with a strange family unit, as long as there is no legitimacy for it? Think about how he would feel when two dads come to his graduation party.
And would you also hand over a child for adoption to an alcoholic? And to a mother and father who are siblings? Or a mother and father who are father and daughter?

When people come to create such a strange family unit (from the environment’s perspective, and also in the sense that this is something new and there is some logic to the idea that two parents of the same sex could cause conflicts for a child), they need to research how a child grows up under such conditions, and there is a feeling — I’m not sure it is factually correct — that there are ideological biases in the studies in favor of the LGBT community, and that it is not politically correct to say that research has proven this to be problematic for the child. (For anyone who remembers the uproar over the researcher who said that all Jews share a common gene, even though that was simply what his research found.)

Therefore, in the adoption issue one cannot ignore the broader context of the matter, because the moral issue (or halakhic, in your view) lies at the base of the topic.

That is an irrelevant argument. Examine each couple and each environment on its own merits (in any case there is a committee that checks this). There are environments in which this is no longer a problem.
By the same logic, you could forbid religious people from adopting because secular people make fun of them, and vice versa. And likewise fat people, because people will mock the child because his parents are fat. That sweeping claim is not substantive and therefore not acceptable.
That is assuming the facts on which people rely are reliable. In any case, the state or the court cannot reject studies without reason just because there are biases (and indeed there are). At most they should present opposing studies. As far as I know, no such studies were presented there.

A. For that you need to know how to balance things. There is an unpleasant feeling that some things are within the norm and others are deviations, and I am convinced there is definitely serious weight to not sending a black African child for adoption into an environment known not to accept people who are different.
B. The other issue is that it may very well not be healthy for a child to grow up with two parents of the same sex. I do not know what is accepted in matters like these, but if experiments on new drugs were conducted at the same level as the experimentation involved in this sort of adoption, they would not even make it to the approval committee.

In any case, because of the bias in the studies and the atmosphere surrounding the issue, the adoption issue goes hand in hand with the moral issue, and therefore usually someone who opposes legitimacy and public recognition for such marriages will also oppose recognition of adoption of children by them, even though the issues do not necessarily overlap.

Obviously I am speaking about the current situation. If in the future this becomes completely normative, then my arguments would be null and void.
It seems to me that the Rabbi also understands that mocking a child because his parents are religious / socialists / leftists / atheists is nothing at all like mocking him over something more intimate, such as his parents’ relationship.
When it comes to views and opinions, it is different.

And the fact that they do not allow one parent, or 3, or any other real number of parents (actually, let it be complex too) — that is fine? What is the difference? Should every case be checked in a pedantic way and then decided whether it is suitable?

Family is a social institution, and society has a conception of what a family is. Israeli adoption law reflects a conception that a family is made up of parents who are a man and a woman. Recently there was a wedding in the U.S. of 3 men, and that reflects a different conception (and note that this was not 2 weddings between one man and two other men, or 3 weddings among all three pairs, but one three-way relationship system; that is, it is not similar to polygamy but something entirely different). I do not think there is any right to adopt. Adoption is society’s concern for children who have no family, and within that framework it does so in what it sees as a family. If someone has a different conception of family, that does not give him a moral or democratic right to receive a child for adoption. If someone is not allowed to bring a child into the world, or is discriminated against in the right to buy a child (as far as I know that is possible only through import), then one can talk about discrimination and harm — but not in adoption.