Hey Peace Promoter,
I might be like too late in marking my point here but still I just wanted to put froth my point as an HR which might help you analyze the problem from a bit different point of view. I went through the whole discussion (majorly) & would honestly like to admit that please understand the point of view being an interviewer here. Being an HR myself, I would like to put forth how your actions might be interpreted (trust me it's nothing to do with religion in most of the companies they are just looking for a good candidate who can make profit & that's it). Hopefully, this angle might help you.
Case 1: If you deny to shake hands, would sound rude (probably because of which you said that you were rejected) & psychologically interpreted as the candidate is being adamant & hence might not adjust in the environment of office. So, probably for the work environment sake one might not pick you up. (This case applies if you do not justify or do not get chance to justify your action)
Case 2: If offered to shake hand from a female interviewer, you acknowledge it either with Namaste or Aadab & then mentioning the reason in short (Nobody has time esp during interview for that long explanation, make it short & simple). It would be a bit difficult to digest as ,like one of the members mentioned it before, usually the muslims are not seen doing this esp in India hence interviewer might be skeptical about it. And on top of that just denying it from female interviewer would be interpreted as chauvism instead of religion. Hence, put forth your point very properly (this would be the turning point as how you might put forth & also, keep in mind that here you're representing your religion also.If the interviewer understands & is unbiased they would definitely judge you on your interview.
Also, most certainly you should be clear of all the things like Namaz time daily & Friday offering etc., you specified in your queries, beforehand only.
Mostly the companies do not fear keeping a good & ardent follower of religion but instead they fear if we give leverage to one others would even come up with one or other thing so you need to be clear that if required or time exceeds you would compensate. So being an HR my problem would be to keep all in one level so that none feels that the other is given more even though I am old employee or may be more experienced etc.
I hope you can see your problem here from this point of view & then look how you should move forward. There are lot suggestions you have got by all intelligent people so you have loads of choices for solution here. Please see it once from this point of view (probably that's what is the significance by putting forth your point here.)
Hope you would have got a job by now where you can follow both your religion together. :)
Best Wishes,
Axita