As with any travel - exercise precautions you would at home, don't walk down dark alleys (literally and proverbially). Speak to local Jews if possible, ask advice in your hotel in advance and when on the ground, if a situation feels wrong, listen to your gut.
Undoubtedly, choosing to mark yourself out as Jewish is likely to put you at a slightly higher risk anywhere you go in the world - and in a country with 140m Muslims - a religion whose book contains explicit hatred towards Jews, as we know - eg from the Koran:
"7:166 Jews are apes"
"4:160 Jews do evil"
"9:29 Fight and subjugate the Jews"
...the risk in India is likely to be slightly higher still.
I have visited Bangalore and whilst it is mainly Hindu there is a significant population of Muslims.
The key question is what is more important to you - keeping your outwardly Jewish identity intact whilst in India and being at slightly higher risk. Or lowering that risk by keeping a lower profile?
Personally, I think there is no shame in the latter, but only you can answer this question.
EDIT My personal experience in Bangalore was that people were friendly if curious - including Muslims. I saw no obvious discrimination against Jews (or others) - but also remember seeing nobody openly dressed as a Jew.
If I had to guess I would say the risk of trouble was low, but not non-existent.