At the risk of over simplifying, an examination of 1 Corinthians 10 could be useful for this discussion. A thorough study is beyond the scope of a post (and should probably include chapters 8 and 9), but Paul seems pretty clear that Christians should not participate in the worship of idols, both for our own sake that we keep faithful to God, and for the sake of others that they not be encouraged in thinking that worship is simply worship and the nominal addressee of that worship is unimportant. Especially the witness to weak Christians is to be considered.
How this works out in specific situations can be difficult. Not all situations are created equal. Some observers may missinterpret the intentions of the Christian (in many different interpretations of the same event) and situations may be entered into thinking one sort of situation is intended and it end up something altogether different. Things are not always what they seem and intentions can at times at least explain if they do not always excuse mistakes.
I think, I hope, that we can all agree that no matter what the event or why a Christian is at that event, a Christian will not direct his/her worship and prayer to any intended recipient other than the one true God, the God of Abraham, Issac, Jacob and Paul, the God most clearly manifest in the person and work of Jesus, the Christ. What others are doing around the Christian, and why the Christian is there is another matter - worthy of discussion perhaps. But a Christian should only intentionally worship and pray to the one true God. The problem with rushing to judgement of others is that we may not know all the facts and intentions and things may not always be what they seem on the surface.
(As an aside, it should be obvious that no one and no thing can prevent God from hearing the prayers of a Christian no matter where or what the situation. For that matter, can we lay to rest the idea floated [not in this forum, I think] that God does not hear the prayers of non-Christians? How could He not hear them, being omniscient and all? What He does with what He hears is His concern and I won't try to tell Him what to do. Besides, don't forget Matthew 5:45.)
Can I pray to the one true God in the midst of people praying to false Gods? Certainly, and God would certainly hear me. Whether He would be pleased with me being there is a more complicated and difficult question. And certainly one on which sincere Christians may disagree. For Christians to raise questions and make suggestions is certainly in order and we encourage each other to faithful worship, service and witness. But let us not forget 1 Corinthians 10:29b, "For why should my freedom be judged by another's conscience?" and Romans 14:4 "Who are you to judge someone else's servant? To his own master he stands or falls. And he will stand for the Lord is able to make him stand."