Break Free CLP is an excellent product. That wont hurt the sewing machine in the least. We were much more concerned with the 3-IN-1 or WD-40. Those two will cause problems down the road.
I have also used Liquid Wrench penetrating aerosol in stubborn stuck up machines without any damage or unwanted problems too. I've been told by many this stuff is bad ju ju, but I've yet to see any.
The trick is once you get the machine freed up, to oil it thoroughly with sewing machine oil to flush out the other stuff.
Joe