it's not about the word itself, it's about how you use it.
generally you say "forget you" to someone you don't like. however, let's say someone (typically someone you know and are friends with) makes a joke about you. to that you could respond, "forget you," but it's in a joking, sort of playful way.
"ayy, forget you man!"
the difference between this and monday is, in my opinion, the hard "er" sound. monday sounds harsher than brother because the word itself just sounds harsh. brother isn't quite as hard sounding as monday. in general it depends on the context. monday in relation to a black person is usually used in a context of hate. "he's just a dumb monday," or, "that monday's taking my tax dollars." however, this is not the only way you can use monday. i generally use monday in a completely joking way. examples could be "stuff monday, what are you doing?" or, aimed towards someone that has any pigment but brown in their skin, "you dumb monday." the latter example is usually used to garner laughs amongst your peers who are also okay with the use of the word in said context. they may even use it jokingly themselves, which can only increase your popularity within your friend circle.
let's move on to brother. brother is typically used to refer to friends or other people in a casual manner. you could say, "what's up, mah brother?" or, "look at that brother over there!". i honestly can't think of any way of making it sound offensive without using it in a sentence like, "i hate that brother," and that's a good thing. you can't say "brother" and sound offensive at the same time without the proper context around it. this makes brother the opposite of monday. while monday has a harsh and sometimes almost rude tone, brother has a lighthearted and, for lack of a better word, friendly tone.
no matter which word you say, it's always about context and tone. through text, you can't really convey tone, since that is conveyed by how you SOUND when you say something, but reading and getting the context of a sentence is usually enough.
it's sad to see sensitive tumblrettes toss around buzzwords about how bad using these words is when they don't understand HOW to use them.well mondays, that's it for today's lesson in english 101. i hope you've learned everything you could about monday usage and monday theory. the test is tomorrow.