I figured I would post the answer since I figured it out. If I add the line
binaryImage = imcomplement(binaryImage)
in it inverts what is black and white and that works for this. It apparently wanted to have the objects be white and not black (?) which is a bit confusing to me, but it works now.
Full code:
image = imread('Gaussian.jpg'); % load in your image
binaryImage = im2bw(image, 0.5); % converts image to binary file
binaryImage = imcomplement(binaryImage) % inverts black and white
BW2 = bwareaopen(binaryImage, 150); % removes objects comprised of < 150 pixels
imshowpair(binaryImage, BW2, 'montage') % display both images to see if spots are removed

