The word necessitates seems overly formal for such an admonishment. Better to be more direct, I think:
Be polite! Don’t raise your voice when you’re talking to the elderly.
(Incidentally, it’s “the elderly” when referring to the group as a whole, or “an elderly person” if you are referring to just one. You could also say “an elder” but that’s somewhat ambiguous, because, strictly speaking, a 13-year-old could be an “elder” to an 11-year old.)
If you want to stress a need somehow, you can lengthen this a little bit:
You need to be polite and not raise your voice when talking to an adult.
Lastly, if you really wanted to keep your original sentence structure, you could use dictates instead of necessitates. I think that’s a better fit:
Politeness dictates not to raise your voice when you’re talking to a woman.
I found this definition in Wordnik that describes this usage of the verb dictate:
dictate (v.) to be the determining cause or motive of; fix or decide positively or unavoidably: as, his conduct is dictated by false pride.
For what it’s worth, an ngram shows a modest number of hits for the phrase politeness dictates, but none for politeness necessitates.