Consider:
I am awesome.
This is a general statement of my state, claiming that it is awesome.
I start being awesome.
This is a claim that I move into the state of being awesome; I was not awesome before, and then I am. It also suggests a degree of agency (I am active in being awesome).
I am being awesome.
This is a rephrase of the first using a doubling of to be to add an emphasis on my agency in being awesome. It's rarely sensible, often awkward, and once very controversial even in more complex forms ("You will be glad to hear, under my own hand (though Rice says we are like Sauntering Jack and Idle Joe), how diligent I have been, and am being." - Letter from John Keats to John Hamilton Reynolds, July, 1819).
Here Keats at least has the excuse that he wants to combine both "have been" and "am being", though some would still say he should have said "...how diligent I was, and am".
Now consider:
When I'm sad, I stop being sad and start being awesome instead.
Standard English, and reflecting a degree of agency, along it being a change of state.
When I'm sad, I stop being sad and am awesome instead.
A change of state is implied by the rest of the phrase, but not by "am awesome" itself. There's nothing to hint at a degree of agency other than it being claimed as a general policy toward sadness. There's a clash between "stop being" and "am", bordering on syllepsis.
When I'm sad, I stop being sad and be awesome instead.
A stronger emphasis on agency, and combines both a claim to always be awesome and a claim to actively be awesome in response to sadness. Be is clearly not used normally, but favouring it over am ties it to the earlier being in a use that again is close to syllepsis.
It's certainly not playing by the rules, but that fits the character, and it's all the more effective for that.
Press the point in this case means:
Keep making an issue of this point.
or
Continue bringing this point to people's attention.
The point they are referring to is the hiring of non-white models. It is not a physical location, but rather a "talking point" or an issue that is being discussed.
It's point as in the expression, "Get to the point."
Best Answer
Typically, the phrase is meant to convey an attitude of modesty and humble gratitude.
Example:
Guy: You've outdone yourself, Gretchen. This dinner is out of this world.
Gretchen: Oh stop it, you. You're too kind.
The meme you linked to expresses the same sentiments, but the context is ironic or absurd most of the time.