this natural gas pipe comes out of the wall to the back of my stove. The other side of the wall is the brick exterior of the home. However the previous owners didn't add on to the house like a porch that is only zone heated with electrical heat when desired. That means the other side of the wall is very cold during the winter. I can often feel a draft coming out of this area around the pipe. My question is is it safe to fill the gap with something like big stuff gap filler or is there something better to use. I'm mostly concerned about it being a gas pipe but I could just be overthinking it.
Yes, it is always a good idea to fill any opening that may cause a draft. The opening isn't wide enough for the use of an expanding foam.
Instead any type of latex caulking will work as would any type of Spackle or plaster.
Use a putty knife (or similar) to press the material fully into the opening.
None of what ever fill you decide on will effect the gas pipe.