Hi Chris,
You don't need them in the same projection.
The first thing I did was plot the data with the imported shapefiles as a visual check:
plot(DATA,col=c('red','blue'),SP=coast,col.SP='grey') # everything seems to be inside a polygon?
plot(DATA,col=c('red','blue'),SP=coastNA,col.SP='grey') # looks good, as far as I can tell
I don't know what anything is, but the second one looks like something, so I went with that.
I then calculated AKDEs and a PKDE just with SP=
coastNA and they both looked okay to me.
But, in your code, you do a bunch of extra steps with raster, sf, stars, and I don't see anything in the sp::plot of the output tstUTM object before akde and pkde are called.
Best,
Chris