Judaism, Christianity, and Islam are the 3 big Abrahamic religions. Theoretically they should all be "competing" against each other. However Judaism gets a pass because traditionally it is not a proselytising religion, one that attempts to convert other religious people or non-believers into Jewish people, while Christianity and Islam do have that history (sometimes forced conversion, conquest, etc). Both old school Christianity, and Islam are "intolerant" of the presence of other religions ( it is a 0 sum game).
In the US, if you are evangelical Christian, see the US as Christian nation, Islam is a threat while Judaism is not. And following the rule "the enemy of my enemy is my friend", Israel is our "friend". That is again, only if you view, we are living through a religious-war glasses, and both Christianity and Islam are both fighting for the same souls, same land. It is not old history either as there is conflict going on in some African states between Christians and Islamic groups, as well as Christian minorities in Islamic states. I should point out in the same way there are fundamentalist Christians and garden variety Christians, there are countries in which Islam and a modern way of life, rights for women, freedom of religion co-exist (Malaysia, Morocco) and other countries or groups (i.e. Taliban) where there is no room for even moderate strains of the same religion to exist.