A common question asked of Unitarians by Trinitarians, especially in the context of a debate, is whether we consider Trinitarians to be idolaters. To be sure, some Unitarians would simply say, "Yes", and end the discussion, but the topic requires a bit more nuance than a simple "yes" or "no" answer provides.
The Biblical concept of idolatry is a broad topic. It definitely encompasses what could be called "base" or "naïve" idolatry - building images, and worshipping them as God (Exodus 20:4-5, Leviticus 26:1, etc.). The principle that the commandments prohibiting this type of base idolatry establishes is that things other than God should not be worshipped as God - the created should not be worshipped in spite of the Creator (Romans 1:25).
There is also arguably a looser sense of the concept of idolatry in Scripture, as in the case of when a person has given their desires an absolute preeminence over their will. In this sense, the Bible describes people "whose God is their belly, and whose glory is in their shame, who mind earthly things" (Philippians 3:19), and speaks of "covetousness, which is idolatry" (Colossians 3:5). This looser sense of the word that may be argued for is not what is being discussed here. Trinitarians are concerned with whether Unitarians consider them to be committing the basic kind of idolatry condemned in the Ten Commandments, for instance.
In response, from a Unitarian point of view, one would have to say that if the term "idolater" can be applied to any who consider someone who is not actually God to be God, then yes, Trinitarians unfortunately do fit that description, as they consider Jesus Christ, who is not God, to be God.
However, this requires some important qualifications. The Bible teaches that Jesus Christ is a proper object of religious worship (Philippians 2:9-11, Hebrews 1:6, Revelation 5:8-14). In what sense is He being "worshipped"? He is being honored as the Messiah - the anointed of God, and the Son of God, and the honor being shown Him is ultimately, "to the glory of God the Father" (Philippians 2:11). Trinitarians certainly show honor to Jesus in this way. However, they have a misapprehension as to who Jesus is. This cannot be considered the same as the types of base idolatry which are primarily being condemned in the Bible - worshipping Pagan gods like Baal or Molech. It is incorrect to consider Jesus to be God, and it is not a good thing. However, it is proper to honor Him as one's Savior and Lord, and praise Him for what He has accomplished for us, and Trinitarians do this.
So, with respect to someone who considers Jesus to be God, it seems like it is too simplistic to label them "idolaters" in the sense that would group them in with the worshippers of Baal, or stone images. It is simply a different situation for which there is no direct Biblical parallel. Although it is wrong, and can be called idolatry in a technical sense, there are several important qualifications that need to be mentioned if the discussion is brought up, to avoid alienating and dismissing someone in an unfair or uncharitable way.
With respect to the Holy Spirit, the situation is even less simple. Most Unitarians believe that the Holy Spirit is generally describing the power of God, and acknowledge that the term is used in very diverse ways, especially in the New Testament. So, in the case of a Trinitarian, they would be mistakenly personifying the power of God, and then worshipping it as a separate Person within God. This is admittedly very confused, but it simply cannot be mapped onto the base forms of idolatry that are the primarily the subject of the Bible's condemnations. It is a Biblically unprecedented phenomenon. Is it confused? Yes. Is it an error? Yes. Can it be called "idolatry"? Perhaps in the technical sense that one is worshipping someone who they suppose to be different from the Father as God. But again, this requires nuance, and is different from worshipping Pagan deities.
While God is the Father, and not a Trinity of Persons, the common form of Christian Trinitarianism involves three Biblically good subjects - the Father, the Messiah, and the Spirit of God. A Trinitarian misconceives of how these three fit into the proper worship of God, and mistakenly believes that the Messiah and God's Spirit are Persons within God, who may be worshipped as God. While this can be labelled "idolatry" in a technical sense insofar as they are worshipping and considering other than the Father to be God, it is too simplistic to attempt to map this directly onto the worship of Pagan gods, or of images of stone. There is no direct Biblical parallel for the phenomenon of the Trinity.
Unitarians should exercise patience and carefulness when discussing this subject with our Trinitarian brethren. It is very easy for a discussion on this subject to devolve into bitterness and alienation, wherein the other person is treated far too simply, and dismissed flatly and without the nuance required by the unusual and complex nature of this topic. If this topic is approached with care, and in an irenic spirit if and when it does come up in discussion, then it will serve as a good testimony to the fact that differences in positions can be clarified on important theological topics without malice or undue offense, and that should always be our goal in dialogue (2 Timothy 2:24-25: 1 Peter 3:15).