How Christians are expected to accommodate or view the existence and presence of other religions vis a vis Christianity? We as Christians acknowledge the God’s plan of salvation at work first through Judaism  in OT and then through Christianity in NT. So this question does not apply to Judaism.
This plan of salvation right from man’s fall in Genesis to the NT, is like a well oiled machine, where the OT and NT are in sync with each other. This I am saying because we accept OT in same spirit as NT and Judaism as from God because that is how God wanted to mould Jewish people to make them ready for receiving His promised Messiah.  Contrary to this we find all other religions not at all compatible with each other and that applies their relation with Judaism and Christianity also.
So what would be the best viewpoint to take on these other religions? How Christians are expected to accommodate or view them vis a vis our belief. Do we have to treat them as teaching that did not have origin from God but only from human thinking or from some hallucinations?
I am looking for answers from the Christian point of view only and not from any other position of belief/unbelief.
Are all other religions man-made?
I'm going to answer the main portion of the question from a purely Biblical perspective.  I anticipate that this question as well as this answer is going to generate a lot of debate, so I'm framing my answer as one from an in-arguably Christian perspective - one that's based on Scripture.

The presence of other religions is addressed in Romans 1.  (Quote below is KJV)


  20 For the invisible things of him from the creation of the world are
  clearly seen, being understood by the things that are made, even his
  eternal power and Godhead; so that they are without excuse:
  
  21 Because that, when they knew God, they glorified him not as God,
  neither were thankful; but became vain in their imaginations, and
  their foolish heart was darkened.
  
  22 Professing themselves to be wise, they became fools,
  
  23 And changed the glory of the uncorruptible God into an image made
  like to corruptible man, and to birds, and fourfooted beasts, and
  creeping things.


In short, man decided to reject God, and searched for other gods fashioned after their own imaginations.  The Biblical answer to your question is that yes, all other religions are man-made.  



*And yes, I realize that there are plenty who would say Christianity is man-made as well, but that's not what the question is asking.  Answers on this site are supposed to represent a Christian perspective, which is what this is, and is what the question specifically asked for.  Whether or not this perspective is true or not is off-topic for this site.*