>>> They ask their god for advice and guidance, and claim to receive responses in various forms.
I think you taking it too literally. When religious person says "God blessed me with the gift of children", they rarely mean that the God - as an actual supernatural being - came to them in person and produced their children as a gift. Most probably, they know exactly where the children come from, and were actually present when those were conceived and born, and even though God might have been mentioned on both occasions, rarely they would claim The Almighty was personally present there and did the work. It is a metaphor expressing the idea of the Providence and God's control and responsibility about what happens to people. In the same way, when they say "I prayed and God let me see the solution of my problem", they rarely mean God personally came down to them in a burning bush, spoke to them and gave them detailed step-by-step instruction of how to solve their problems. Etc., etc.
>>> Prayer is functionally indistinguishable from divination.
Prayer is nothing like the divination. Prayer is an expression of certain feelings or formulae about the supernatural. Divination is a mechanistic procedure in which one would, after performing required ritual, receive information about the future or otherwise inaccessible information. Of course, you can pray for success of your divination, or you can try to divine if your prayer would be followed by some event, but those are two functionally very different actions. Note that for prayer, one usually is required to be a believer, while for divination you don't really have to believe in anything as long as you perform the ritual properly. This, btw, is a big different between modern religion and old religions - most of the old religions couldn't care less what you think as long as you do proper procedures. Modern ones rather concerned about morals and feelings and beliefs and all that immaterial stuff.
>>> I have, on more than one occasion heard protestants describe various aspects of Catholicism as witchcraft and idolatry.
I have heard the whole Christianity described as idolatry. So what? The question if Christianity is idolatry or not from the POV of anybody is not the question we were discussing.
>>> whether it is acceptable to ask them to pray on your behalf
I can imagine how it may be a problem for an ostensibly monotheistic religion, but that does not make a prayer a divination. Of course, that does not mean actual Christians never engage in practices which are, in fact, divination - but people violating the premises of their own religion is nothing new. I can give you Jews eating pork, Muslims drinking wine and Christians hating their fellow man. It happens. However, the religion as a belief system and as a social mechanism does not endorse it.