There is no prohibition against using the sign of the cross as a Protestant. Yet, there is no Biblical command to use it either. The same is true of closing your eyes when you pray, and even praying before meals.
Yet, the sign of the Cross, as I understand it, is used at the close of prayers. We are commanded to pray in the Name of Jesus, but not that of the Father and the Holy Spirit.
"Until now you have asked nothing in my name. Ask, and you will
receive, that your joy may be full." John 16:24 ESV
However, we are commanded to baptize in the Name of the Father, Son, and Holy Spirit.
"Go therefore and make disciples of all nations, baptizing them in[a]
the name of the Father and of the Son and of the Holy Spirit."
Matthew 28:19 ESV
So, praying in the Name of the Father, Son, and Spirit actually seems to be somewhat contrary to the command of Jesus. We pray in the name of Jesus and we pray to the Father. Adding the name of the Father and Holy Spirit is, again, not specified in Scripture, so it's likely just a tradition of men.
Consequently, a reasonable conclusion to draw is that if we are commanded to pray in the name of Jesus and not in any other name, including that of the Father and the Spirit, then that is probably what we ought to do. Had God wanted us to pray in the name of the Father and of the Holy Spirit in addition to the name of Jesus, it seems He would have mentioned that when He told us to pray in the name of Jesus.