Great question! I can handle the ancient parts of this question, but I'd love it if experts on Christian demonology or Fundamentalist rhetoric could answer more fully on later periods.

Let's start by taking our terms apart in turn.

Ba'al/Baal (בַּעַל) is a common ancient Hebrew word meaning owner, lord, or master. In the law (e.g. Exodus 21-22) it usually refers to legal owners of things. In a political context, it usually refers to the nobility/leaders of a town or region (e.g. 1 Sam 23:11-12, 2 Sam 21:12, Isaiah 16:8). In the context of marriage, it refers to the husband (e.g. Isaiah 54:5).

Baal is used throughout the Old Testament in a variety of ways, including as a plural for various gods apart from Yahweh (e.g. Judges 2:11), but often refers to a particular deity, most often Baal Hadad, a popular storm god. Baal Hadad is the antagonist in the story of Elijah, which climaxes in a contest between Yahweh and Baal atop Mt. Carmel in 1 Kings 18 to see who truly controls lightning (to light the altar) and rain (to end the drought).

Moloch/Molek (מֹלֶךְ) is a vocalization of the Hebrew letters MLK, which are the same as melek (מֶלֶךְ king) or malak (מָלַ֖ךְ reign). Hebrew has no proper vowel letters, and so the vowels we use are generally sourced from the Masoretic Text, a medieval Jewish rendition of the Bible in Hebrew with vowel points (the tiny dots on next to the letters). Some scholars have proposed alternate derivations, but the simplest and most widely accepted answer is simply that the word comes from the root for King/Rule.

But here's the tricky part: it's not clear if Moloch was an actual deity or if it's a misunderstanding on the part of later interpreters. Hebrew uses prefixed prepositions to convey ideas like to/for (L), as/like (K), in (C), or from (M). We almost entirely encounter Molek in the form La/LeMolek or "to Molek," and almost entirely in the context of child sacrifice. Lev. 18:21, 20:2-5, 1 Kings 11:7, 2 Kings 23:10, Jeremiah 32:35 refer to the sacrifice of children, with most specifying "in fire." Amos 5:26 is probably best translated with "king" rather than Molek, and that leaves only one instance in the whole Bible of Molek appearing without the lamed prefix, in Leviticus 20:5, where the prefix is replaced with the independent preposition אַחֲרֵ֥י (achare, after). Because of the specificity of these references, modern scholars debate whether Molek was an actual diety, or rather just a prohibited form of sacrifice. Human sacrifice was taboo in developed Judaism, and was often interpreted as being abolished in the Abraham/Isaac story, though its earlier existence is suggested by various stories in the Bible including the binding of Isaac and the daughter of Jephthah (Judges 11).

(The existence of human sacrifice in Canaanite religion has been much debated, particularly because the primary written sources for its existence were written by their enemies (Jews for Canaanites, Romans for Carthaginians). There is certainly a great deal of both documentary and archaeological evidence for child sacrifice, all of which has been questioned from many angles. While an interesting debate, getting into such a question is beyond the scope of this answer.)

In any event, monotheists have vacillated ever since between viewing small "g" gods as misunderstood aspects of big "G" God, demons adversarial to God, or simply non-existent. While the point of the Elijah story is that Baal either does not exist or has no real power, later sources do interpret Baal (or the baals in the plural) as demons. Jesus seems to equate another Baal, "Baal Zebul" (Βεελζεβούλ, Beelzeboul) with Satan in Matthew 12 and Luke 11. Jesus' opponents accuse him of being in league with Baal Zebul, whom they describe as "ruler of demons" (ἄρχοντι τῶν δαιμονίων, archonti ton daimonion). 1 Corinthians, an authentic Pauline epistle, may hint at differing opinions on this question in chapter 7, where Paul discusses how eating food sacrificed to idols (effectively any meat outside of Jerusalem) affects the conscience of various people. In later demonology, many different pagan deities were interpreted as demonic figures. (For a particularly vivid look, I recommend Satan's council in Paradise Lost.)

Later, the vivid creativity of authors such as Gustave Flaubert (Salammbo, French, English) and G.K. Chesterton (The War of Gods and Demons) brought a vision of the world of Canaanite/Punic religion into the public imagination. The focus here was particularly on the practice of infant sacrifice.

Here I'm out of my historical depth, but what I do know is that all this got attached to the anti-abortion movement, which has developed a fascination with medical-waste incinerators. The Bible doesn't actually include much of anything to go on if you are trying to argue against abortion, so it was helpful to attach on to the vivid (and terrible) image of child immolation to find a tie to the Biblical text. It's a stretch, to be sure, but when Raphael Warnock calls himself a pro-choice Christian pastor and is accused of Moloch worship, this is what is being referenced.