No, a Catholic should not receive communion in a Protestant church. Catholics believe that Jesus' Body, Blood, Soul, and Divinity is present in the Eucharist during our Communion and that it is not just a mere symbol. This is not the case in non-Catholic churches/denominations that do not have valid Holy Orders - therefore, they do not have the Real Presence of Jesus when they go to communion. To have a valid Eucharist, you need valid priests and bishops - the only other churches that have valid orders are the Eastern Orthodox and even then we can only receive the Eucharist in their churches under very strict circumstances which I will explain at the end.
There are several reasons why a Catholic should never take Communion in a Protestant church, the first is that Communion is a sign that we are one in belief and practice. Since we are separated in our beliefs about what the Eucharist is, Church authority, holy orders, etc. We would be lying with our actions to receive communion in a non-Catholic church. It is as if we believe one thing (we are not united completely in faith and practice) and saying/doing another (we are one).
Catholics who lack access to Catholic Mass may receive communion from Orthodox churches, but most Orthodox will not allow it. Thus, we have to have permission from the Orthodox Bishop or patriarch. Also, if in danger of death, a Catholic can receive communion from another church with valid sacraments, which excludes the Protestant churches. Canon law has the following:
§2. Whenever necessity requires it or true spiritual advantage suggests it, and provided that danger of error or of indifferentism is avoided, the Christian faithful for whom it is physically or morally impossible to approach a Catholic minister are permitted to receive the sacraments of penance, Eucharist, and anointing of the sick from non-Catholic ministers in whose Churches these sacraments are valid.I hope this helps.