A question on Mi Yodeya was motivated by the asker hearing a Jew decline to participate in a Christian "grace" before a meal. This person asked: since Jews, Christians, and Muslims all worship the god of Abraham, wouldn't it be permitted for a Jew to participate in a Christian prayer so long as it's to God and not to Jesus?
Christianity and Islam say they worship the same god that we do, but that does not make it so.
Christianity is the bigger problem. They say that a human being was part of God, which is shituf (think of it as heresy). That means it is forbidden for a Jew to participate in their prayers. On top of that, the trinity concept adds confusion. I am aware that different Christian denominations give the trinity greater or lesser importance. Distinguishing all the nuances calls for more expertise in Christianity than most of us have. It's hard for us, as outsiders, to navigate their theological variations, especially in real time.
Islam is less problematic, in that they don't say that God took human form, but they do sanctify the Christian gospels, counting Jesus as a prophet. Like Christianity, they say that the torah was deprecated or superseded, so they are at least wrong about God, who gave us an eternal torah, as far as we're concerned. Whether that is enough for halacha I do not know, but it is enough for (dis)comfort for many, including the author of the comment you quoted. Some are also concerned about giving the appearance of endorsing another religion.
Even if you think the text of any particular prayer is unobjectionable, carefully reviewing the text (if you can even get it in advance) imposes a burden of both effort and knowledge that many aren't willing to take on. Especially in a social setting where it's relatively easy to extract oneself, like words before a meal, it makes a great deal of sense to do so instead of trying to navigate what is or isn't acceptable.
Besides, in my experience Christians tend to extemporize their prayers, and it's very, very difficult for them to leave Jesus out of it. So your qualifier of "as long as they pray to God and not Jesus", even aside from the other issues I raised, might not stick in the moment. Rarely-needed care almost never wins out against deeply-ingrained reflex, and the phrase "through so-and-so our Lord (sic)" is a standard phrase in Christian prayer.