I find it interesting that these evangelicals are fasting not as a Christian discipline, but rather to show respect and solidarity with Islam. I have several Muslim friends. Were I to announce I would be participating in Ramadan with them, they would see it as the obvious gimmick that it is. Others seem to agree.
I noticed something similar back in the 1980s, when it became fashionable in some Christian circles to hold Christian Passover meals. I did so myself on a couple of occasions, when I was an Angl;ican, and even invited some Jewish friends to join us at one of them. It was in a small town where there was no Jewish community and the Jews who came were generally non-observant, and seemed to appreciate both the invitation and the meal itself, though perhaps they were too polite to say what they thought of the Christianised bits (If he had sent the prophets, but had not become man for us, we would have thought it enough; if he had become man for us and not performed miracles of healing, we would have thought it enough, etc). But my observant Jewish friends were rather horrified when I told them about it, and clearly saw it as the obvious gimmick that it was.
In some ways it was a useful educational exercise, to learn something of the Jewish roots of Christian worship. But it also became clear that it didn't fit.
In our Anglican parish we discussed when we should have it. Some said Maundy Thursday, on the assumption that the last supper was a passover meal. We did that one year, but it didn't feel right to eat meat in Holy Week. So the next time we did it, we did it on Easter Monday. And looking back on it, I can see that St John Chrysostom's criticisms of Judaising Christians were right on the money. The "Christian Passover meal" was a chimera.
And then this year, having just completed the Dormition Fast, I read various blogs where people were urging Christians to observe the fast of Ramadan. I suspect that most of them had never even heard of the Dormition Fast. Though they were Christians, they were more familiar with Muslim traditions than with Christian ones.
So I recommend the whole article Notes from a Common-place Book: A Christian Ramadan?, and the comments are worth reading too. Another thing I discovered a couple of years ago was that some evangelicals were beginning to realise that there was quite a lot in the Bible about fasting, but they were suspicious of the practice because they associated it with asceticism, which they regarded as a Bad Thing. For such people I wrote Christian asceticism: Khanya.
There's also another interesting take on this at The Ochlophobist: ramadan and closet lesbian evangelical zionist dancers; usual ochlophobic topics...