I have an old 30 amp outlet that I was planning to reuse. There isn't a connection for a ground, but since I am connecting to a metal box, I now have a connection between my neutral and ground. Should this cause a problem?
In your other question I commented that due to your peculiar setup and grandfathering, you are forced to tie neutral and ground in your service panel here in the barn. (Normally you wouldn't).
Do not tie it anywhere else! Neutral is not ground!
Now, the socket in this picture is a NEMA 6-30. NEMA 6-30 has a ground and does not have or need a neutral. If that is the socket you want, you are all set. That would be used for water heaters, A/C units, compressors, machine tools and other equipment that runs on a 240V single-phase motor or resistor heating (such as a drying kiln).
This looks like all new work, and I assume that is MC cable. If that cable has a ground wire, you need to use it and not just depend on the metal sheath for a ground path.
Now, if you are installing a NEMA 10-30 (neutral not ground), stop. Do not use NEMA 10 for anything, it is obsolete and it is dangerous and illegal to install a new one. If you have a dryer that has an existing NEMA 10 cord/plug, then install a NEMA 14 receptacle (4-pin) which includes neutral and ground. Get the installation manual and follow the instructions for replacing the NEMA 10 cord with a NEMA 14 cord. (you need to remove the bootleg strap from the machine).
If you are installing a NEMA 14 (or 10) here, and you need neutral, look in that MC cable for a white and red wire. For neutral, you will need a cable that has black, white and red. If that is not present in the cable, then you need to replace the cable run. There is no way to retrofit neutral.
By the way, in these drawings I show both hots as black. Because they are interchangeable, it doesn't matter if they're swapped. The wire is red in the cable mainly because that's how cables are made. In conduit, I would wire it with two blacks.