Does Philosophy undermine religion?

Philosophy doesn't focus on undermining religion, it can't it's a process, some philosophers focus on underminging anything that doesn't fit their myopic view of logic be it religion or anything else, while some people in the guise of philosopher do the same because they found a tool that can be manipulated to make their personal agenda seem credible.

Philosophy only undermines religion when 1) philosophy is misused/misunderstood or 2) when religion is misused/misunderstood.

In the case of 2, philosophy should undermine religion.

Some philosophies undermine other philosophy. Some religions undermine other religions. Some philosophies undermine religion. Some religion undermines philosophy.

Whether something is undermined or not just depends on how intellectually appealing that perspective is to you. But this is nothing new, philosophers have been disagreeing with each other since pre-Socratic times.

To correct, you need to either take "why" out of the conditional statement (because "why" begs the ontology of the "if" conditional and is also syntactically incorrect), or in this instance change "does" to a future tense word, such as "would" (because "does" implies that the "if" clause currently is when in fact the "if" conditional suggests that you do not know something to be or not). Also, there seem to be a few implicit assumptions which, if I may, would like to tease out by reformulating your 'conditional statement':

1. If philosophy is the acceptance of other ideas, values and evaluations on logical principle, and
   
2. If philosophy undermines unacceptable ways of examination, and
   
3. If religion is an acceptable way of examination,
   
4. Then why does philosophy focus on undermining religion?
   

Please let me know if this reformulation is not acceptable to you, Cyber Abyss.

Premise 1 rests it's acceptance "on logical principle," and I believe in itself it is enough to answer the question. Religion is not based on logical principles, therefore premise 3 is false by virtue of premise 1. However, even this being the case, I would still like to make a few additional comments.

Accepting may indeed be the "valuing (and devaluing) of all ideas and not just the ideas that come to conclusions", but valuing does not include that one must accept the truth or falsity of what is being valued. For ideas which you say are 'not just the ones that come to conclusion', I believe one of the major aims of philosophy would be to determine which foundation the value was being derived from and to then place more value in those items which were shown to be closer to what we could consider our best source of indubitable knowledge. A person does not have to know the outcome in the attempt to evaluate the basis of ideas.

For example, mathematical and logical foundations seem to be two of the best explanations for the most amount of data and the most amount consistent results. Thus, if we have a problem lacking a firm conclusion, simply determining which foundation the problem can be reducible too and then holding it's construction up to the standards set by the foundation, we can determine how much the idea is worth valuing.

Religion as a foundation has some of the least capable ability to explain the most amount of data and the most consistent results.

Furthermore, mathematics, logic, the empirical sciences, and phenomenology, for example, seem to have a very easy time in relating to one another. There is mathematical logic, there is empirical and phenomenological inquiry into the nature of mathematics, and the results of one foundation seem to historically have fruitful impacts on each of the others. Some parts of each of these foundations are actually so intertwined with the other foundations that they have created a necessary reliance on the very foundation of the other. Religion does not have this. It does not have to care about logic. It does not have to care about mathematical breakthroughs. It does not have to care about the empirical sciences. Its very attempt to be founded on a god or god(s) severs itself. On the otherhand, these foundations have

Many great philosophers were theistic; equally many great philosophers were not. I do not think philosophy is necessarily about acceptance of all ideas, but I also think both religion and philosophy are too diverse topics to really provide any useful statement about whether one undermines the other, although I think Aedes certainly has condensed a reasonable statement regarding both.