I always used to think the word was ignorant but it has turned out that I am wrong.
The word I would use is rude.
Consider self-absorbed (“Overly concerned about oneself, to the point of ignoring the feelings of others”); inconsiderate (“Not considerate of others, thoughtless”); egotistical (“Believing oneself to be better and more important than others”), and arrogant (“Having excessive pride in oneself, often with contempt for others”).
In the spirit of not being more negative when referring to others than I would wish to be used when referring to me I suggest inattentive is the correct word:
Exhibiting a lack of attention; not attentive
Using neutral terminology encourages you to see communication as a two-way street. Referring to someone with using a negative term implies that it's all their fault and may not encourage you to try to resolve the issue.
Neglector may apply here .
I suggest you use snubber or snob.
Perhaps "deaf" is an unexpected answer. I assume you mean someone who does this intentionally or habitually. In that case "opinionated" might apply. They don't want to hear dissenting opinions, so they ignore them.
Perhaps the noun isolate
a person or thing which has been or become isolated: social isolates often become careless of their own welfare
presumptuous fits the scenario were one thinks so highly of himself that other people opinions or existence are irrelevant. http://www.merriam-webster.com/dictionary/presumptuous
As indicated in the comments above context is everything.
One interpretation of the question is of someone who ignores others in a non-interfering self-centred kind of way - a perfectly rational decision deserving a neutral label. Such a person is an egoist.
the habit of valuing everything only in reference to one's personal interest; selfishness
Another interpretation is of a person who is stubborn in a stupid kind of way, mulishly ignoring other people even when they are more sensible or intelligent than them. Such a person is pigheaded, or an egotist even.
excessive and objectionable reference to oneself in conversation or writing; conceit;
Without context, it's difficult to answer correctly but standoffish works as it's a description that doesn't rely on the person's personality or health status (eg deaf).
Try this experiment on the next stranger you see on the bus who's 'ignoring' others and say to yourself 'that person is snobbish/a snob/reckless/presumptuous' etc which suggests you're aware of their personality. Doesn't work does it?
'That person is standoffish' can be applied to a stranger. The reason for their standoffish behaviour is not relevant, just their current demeanour which you're wanting to describe.