I can't think of one word or phrase that ticks all your boxes. Maybe some combination of the words and phrases below might convey what you want.
Hypocrite or hypocritical might be of some use in highlighting the inconsistency of the behaviour in ignoring some people but not others:
a person who claims to have certain moral principles or beliefs but behaves in a way that shows they are not sincere
User Valrog suggests biased above - a perfectly good answer.
In a very similar vein, bigot or bigoted might work - they are somewhat stronger than biased, and suggest an unreasonably closed mind, rather than a mere partiality one way or another:
someone who is bigoted has opinions that most people think are
unreasonable, especially about politics, race, or religion, and
refuses to consider other people’s opinions
To get more specific, if it is a sex-based discriminination, which you seem to suggest might be the case, the person in question might be called a chauvinist. (I think the noun is more commonly used than the adjective, chauvinistic.)
someone who believes that their own country, race, sex, or group is
better than any other; this word is used especially about men and
their attitude towards women.
Another idiom that might work for you is:
to choose very carefully from a number of possibilities; to be
You must take what you are given. You cannot pick and choose.
Meg is so beautiful. She can pick and choose from a whole range of boyfriends.
Selectively deaf or selective hearing also might describe one aspect of the situation in your question. This phrase hasn't made it into the dictionaries yet, but I'd think it would be generally understood.
Both the excerpts below try to put selective deafness in a scientific context. However, the phrase as usually used is heavily sarcastic, implying that there is no actual deafness at all.
"Did you hear me?" It's a question that many an exasperated wife has asked her husband.
By Stephen Adams, Medical Correspondent, 27 May 2011
The question is usually delivered in ironic fashion, because how could
he not have heard her request to unload the dishwasher? Does the
newspaper really rustle that loudly? But now men have an answer to
the charge that they are 'selectively deaf'. For scientists at
University College London have discovered that people really can "tune
out" the sounds around them to concentrate on the matter at hand...
Why can your partner never hear the phone ringing? It could be that their brains are wired to ignore some sounds.
We can all recall times when we were so engrossed in something that we
were oblivious to our surroundings.
Regularly recurring sounds also often don’t register, especially if
they don’t require any reaction from us. An example is people living
next to a railway line who don’t hear the passing trains anymore.
There’s a difference between physically hearing a sound and
consciously registering it. To put it simply, you “hear” what you
focus on or pay attention to – even if you choose not to react. A case
in point is when someone at a cocktail party manages to drown out the
peripheral noise to have a conversation with one or two people.
Selective hearing is not necessarily a case of people pretending not to hear, it’s actually a way for our brains to filter out extraneous
noise so we can concentrate on what’s important at that moment.
(Emphasis in the quotes above is mine.)