I have four allays with me in the overworld all carrying blocks. I placed them in a tunnel and closed them in so they couldn't get out. Then, I went through the nether portal, and once I was in the nether, the four allays teleported with me. When I went back to the overworld through the portal, they all returned. 

This time, I tried the same thing but removed the blocks from two of the allays in the tunnel, keeping two allays remaining with blocks. I went through the portal into the nether, and the two block-holding allays teleported with me, leaving the other two allays without blocks behind.

This is a big issue for people who want to make allay storage, item sorters, or have item transportation in their worlds since people will give their allays blocks, travel to the nether, and have all of those allays carrying blocks be teleported with them.