The phrasal template "miss me with that/the…" has been a slang staple for years now, equivalent to "don't give me that…". A common variant is "miss me with the bullshit". Several examples can be found in rap songs, especially in the last few years. The earliest I could find is this line from Drake's 2010 song "Light Up": "Y'all can miss me with the money talk".
The most popular variant today, however, is "miss me with that gay shit". Google Trends suggests it started showing up in 2014, but it didn't kick off until recently.
[direct use of the Google Trends embed code is no longer allowed]
Link to what I tried to embed.
On May 13, 2015, Vine user Dope Island posted this Vine called "Homophobic kindergarten teacher" which uses the phrase "miss me with that gay shit". It has reached 9.2 million loops. A repost on YouTube called "Miss me with that gay shit nigga" seen below currently has over 200,000 views
It has been used as a sound clip in other remixed videos on YouTube. In fact, this isolated clip uploaded as a "sound effect" has over 100,000 views.
However, the main reason I'm making this post is to highlight a series of image macros that have cropped up in the past year. In a manner similar to Respect Women, objects are labeled "me" and "that gay shit" to imply that the user is either avoiding or embracing the gay shit depending on the image.
One recurring screencap with this phrase comes from Gravity Falls short "Mabel's Guide to Color" in which Dipper holds up a mirror to deflect a rainbow.