At times, philosophy overlaps with other disciplines. On some accounts of what philosophy is, philosophers should be totally open-minded about all possibilities and only settle on a belief once ample reasons have been given for believing it. Religion, however, demands faith about these beliefs. Regardless of reasons, a religion wants you to believe what it has to say. Does this mean religious people are at a disadvantage in philosophy? You could argue the following:
1. Philosophers should be open to consider anything
2. Religious people can’t consider certain things
3. So, religious people are at a disadvantage as philosophers
In response to this argument, let us consider a case elucidating the relation between philosophy and science. The ancient philosopher Aristotle hypothesized that what makes statements like Dogs are 
animals true is the existence of dogs and that animal is part of their constitution. However, what about before dogs existed? What would make Dogs are animals true then? Aristotle believed the universe has existed eternally as it is now, so there have always been dogs to make Dogs are animals true. At the time, there was no reason to reject this cosmology, so the open-minded philosopher would have to seriously consider Aristotle’s explanation.
Since then, however, our best science has shown us not only that the universe has not always been the same, but it hasn’t always existed (much less dogs). Is it incumbent on modern philosophers to take Aristotle’s explanation of what makes Dogs are animals true seriously in the name of open-mindedness? The idea seems absurd. The whole theory rests on a cosmology that has been shown to be scientifically false. Not only would open-mindedness not be a virtue here, it would be a vice. Science has done philosophers a service by cutting out philosophical theories that can’t be true. A philosopher would be wrong to reject this just because it came from outside of philosophy. Not only is it okay for philosophers not to be open-minded here, they should be closed-minded. In other words, (1) is false so long as there are good reasons against a possibility, whether philosophical or not.
Now consider the case of religion. Is it true that a religion wants you to believe something for no reason at all? Most religions wouldn’t say that. Most religions want you to believe something because they
believe (i) they have special access to esoteric knowledge and (ii) there are good reasons for you to believe they have this special access. Of course, they could be wrong about this, but the time to be an open-minded philosopher is when considering these reasons. If the religion is right, then just as in the scientific case against Aristotle’s cosmology, philosophers should be closed-minded about contradictory possibilities. So, it’s only the case that a religion could interfere with philosophy if there aren’t good reasons to believe the religion, and whether or not there are good reasons will depend on each religion individually.
What about if the religion is wrong about (i) and (ii)? At this point, the ideas the religion espouses are still a possibility, but we no longer have any reason to reject other possibilities, so open-mindedness would be a virtue here. However, this still doesn’t mean faith is necessarily opposed to philosophy. The believer may to continue to believe, but remain open to other possibilities. In fact, this is analogous to what we do in much science. I might believe in Big Bang Theory over String Theory, but remain more or less open to the possibility that I’m wrong. I might continue to pursue evidence either way, ready to change my beliefs accordingly. In the same way, a religion might provide some reasons to trust it and we may believe it to that extent, while continuing to pursue the truth open-mindedly.
For more, please see my YouTube video “Is faith bad for philosophy?”