The reason for Muslims not joining Christians in prayer is that Protestants pray "in the name of Jesus", Catholics pray "in the name of the Father, the Son and the Holy Spirit", while Muslims pray "in the name of Allah, the Most Merciful, the Most Compassionate". I am afraid that you don't see the distinction that I see, but Muslims don't associate others with Allah in prayer.not able to pray and work alongside non- Christians at the moment.
I suppose when you say work, that you mean charitable activities. From my perspective, Christian charities are almost always associated with "spreading the Gospel" which is something that Muslims can't support.