[Note: As is usual in my 'preliminary musings' posts, this is sort of an initial shooting-from-the-hip type of post. All conclusions herein are highly tentative and more or less un-proofread. Hopefully after more extensive thought on some of the points, I'll be able to write more detailed posts on them. Also please note that this post is directed at a certain particular strand of LDS theological thought, and there may be forms of LDS theology to which many if not all of the following points are inapplicable.]
In a number of dialogues with Latter-day Saints, I've often heard the sentiment initially expressed that they worship the Father but not the Son or the Spirit. At other times, however, I've heard the different message that they worship the Father as the Creator and the Son as the Redeemer, or the Father as the Father of their spirits and the Son as the Savior, or some other treatment like that. As I understand it, the operative concept here is one of 'worship-as', namely rendering worship to a person when that person has earned it by some contingent act, in the absence of which they would not worship that person. That is as best as I can seem to parse the concept in terms of worship simpliciter.
It's very difficult to tell if I've got the idea here, because I've heard a vast number of very confused mixed messages from Latter-day Saints on this issue, and those whom I've asked have often become even more evasive than usual. This whole framework, however, is rather foreign to Evangelical ears. Christians have typically held that God - Father, Son, and Holy Spirit - are intrinsically worthy of worship by all. (In this and hereafter, by 'worship' I mean 'worship simpliciter' in a robust Christian sense, which involves a recognition of the object as perfectly divine and as ultimately authoritative and valuable without external peer.) Worship is not something that can be earned by any act. If God is worthy of worship at all, he is worthy of worship whether or not he does X. If God is not worthy of worship apart from doing X, then he is not worthy of worship with it either. Worship-worthiness is not relative; it is absolute. If an entity Y is worthy of receiving worship from person A, then any person B similarly has an objective duty to worship Y as well; and if B does not worship Y, then B does wrong. And furthermore, because the act of worship is an act of recognizing another as ultimate, then there cannot be a multiplicity of alternative objects of legitimate worship, as there cannot be alternate valid ultimates. This, it seems, is the lofty vision of worship that has largely been upheld by Christians throughout history, and seems also to be at least implicit in the biblical text, as I read it.
And it's in light of this that I think we see why some LDS teachings, both official and unofficial, are utterly unthinkable to traditional Christians like Evangelicals. We do not worship the Son simply because he has saved us. If the Son had never come to earth, he would still have been worthy of our worship in the robust sense above. This is why 'worship-as' has never been a significant concept in Evangelical discourse. Furthermore, it seems to be plagued by additional difficulties: why should certain roles merit worship and others not? Could not a pagan argue that she worships Zeus as lord of the sky, Poseidon as lord of the sea, Aphrodite as lady of love, and so forth?
Also, this shows why the idea of further deities beyond the Father who are allegedly 'irrelevant' to us is so peculiar to Evangelicals. (This idea is affirmed by some but not all Latter-day Saints.) Suppose that the Father also has a Heavenly Father of his own whom he worships as the Father of his spirit. This 'Heavenly Grandfather' would surely be a God in his own right. And with the notion of worship outlined above, it seems as though it would be wrong for any individual anywhere to not worship Heavenly Grandfather. (The same could be said for a slightly more familiar figure in the LDS 'pantheon', namely Heavenly Mother.) Also, if even Heavenly Father considers Heavenly Grandfather to be worthy of worship, how could we not worship Heavenly Grandfather? Another difficulty is that part of true worship is full devotion such that we wish to proclaim the greatness of our object of worship to all. Thus, if Heavenly Father had a higher God to worship, then it follows that if Heavenly Father worships this higher God perfectly, then Heavenly Father would teach us to worship Heavenly Grandfather as well to bring greater glory to Heavenly Grandfather. (Alternatively, Heavenly Father might worship Heavenly Grandfather imperfectly, but this would mean that Heavenly Father is currently imperfect and indeed a sinner at present, which conflicts very strongly with any Christian vision of God, whether Evangelical, LDS, or otherwise.) Even the LDS notion of 'worship-as' doesn't seem, so far as I can see, to deal with this problem, because if the grounds for Heavenly Father's worthiness for our worship is that he is the Father of our spirits and thus our benefactor... well, he could hardly have done this without the prior patronage of Heavenly Grandfather as the Father of his spirits, making Heavenly Grandfather the Grandfather of our spirits - and are we not taught to respect and revere our elders?
And even cutting out the notion of higher deities, consider the instance in which our Heavenly Father is locally highest but has a number of peers elsewhere in reality. Given the notion of worship mentioned previously, there are only a few options. Either they worship Heavenly Father, or Heavenly Father worships them, or they have no such worship relation. We can strike Heavenly Father worshipping them, since that would correspond roughly to the scenario above. If they worship Heavenly Father, then it would seem that they cannot be his peers as deities in their own right, for they would have to insist that they are unworthy of anyone else's worship, which must be redirected to our Heavenly Father. (Note that the scenario depicted in some forms of LDS exaltation eschatology corresponds to the framework established here. If we become 'gods' who give rise to a new generation, then we surely will teach them about our Heavenly Father and direct them to worship him rather than us; to do otherwise would be to withhold glory from him and so to dishonor and sin against him. Thus, it seems that we can never really become 'gods' in the sense in which he is 'God'.) So let us then suppose that there is no worship relation between them. As noted above, if an entity is worthy of worship by some, he/she/it is worthy of worship by all, such that failure to do so is a serious wrong. Thus, if there is no worship relation between them, then either the other deities are sinners and therefore not gods at all, or else our Heavenly Father does not merit our worship either, which is false.
As said before, these are some reasons, I think, why Evangelicals may have a difficult time entering into this particular LDS mindset on worship, which certainly appears to offer a significantly minimized view of God in comparison with that found in traditional Christian theology.