No, Christians showing compassion for Muslims could be because the love of Christ for lost sinners dwells in the hearts of those who have, by His grace, come to know Him. Inviting Muslims or any other lost persons to church doesn’t necessarily mean the message of the gospel is being compromised. Just maybe, it’s being fulfilled.
Not in this scenario.
And guess what kind of “love” the Mahometans would show them if they did not have who they both regard as their common foe?
Not to mention, the Gospel is meant to be a witness against mankind and mankind’s errors. The Mahometans insist that the Injeel (Gospel) that the Christians observe has been corrupted and any “witness” to the contrary is regarded by them as blasphemy punishable by death.