Does the Hellsing Organization belong to the Anglican Church or the Protestant Church? Or is it a secular organization?
The Hellsing organization is part of the Anglican Church. Whether the Anglican Church is Catholic or Protestant is a bit of a complicated question.
To start with, while there is a "Catholic church" (it's the common short name for the Roman Catholic Church in English), there's no corresponding "Protestant church". There are multiple Protestant denominations, many of which have sub-denominations, many of these having multiple churches within them: Lutheran, Presbyterian, Baptist, Pentecostal, Methodist, and lots of others. All of these groups have their roots in Martin Luther's Protestant Reformation, which began in the early 16th Century in Western Europe in response to perceived corruption and doctrinal inconsistency in the dominant Roman Catholic Church. All the early Protestant churches had certain Roman Catholic practices they objected to; Wikipedia has a good summary, but in general the Protestants thought religion should be less focused on worldly matters and more focused on faith and prayer. They also rejected the authority of the Roman Catholic pope and focused on the Bible as the single defining document of Christian belief, whereas the Roman Catholic Church had elevated various commentaries by popes and other prominent figures.
Anglicanism existed as the English branch of the Roman Catholic Church until 1534, when the English parliament declared Henry VIII, the King of England, as head of the church. This split the leadership from the Roman Catholic Church, but theologically, the Anglicans continued to keep the Eucharist, which most Protestant churches had abandoned. Whether this makes them Protestant or not is a bit hard to say. They are often considered Protestant because they split from the Roman Catholic Church in the same period when the Protestant Reformation was going on, but the split had no real connection to Luther's movement; it was a political maneuver by the English government to weaken the power of the Roman Catholic pope. Theologically, they're more similar to the Roman Catholics than most Protestant churches are (though as we see in Hellsing, they still find enough differences to keep them arguing).
As a point of interest, there are Christian churches which are neither Catholic nor Protestant: for example, the Eastern Orthodox churches, which include the Greek Orthodox and Russian Orthodox; Ethiopian; Coptic; and various modern movements such as the Jehovah's Witnesses. So you could argue that Anglicanism is neither Catholic nor Protestant, but something distinct, like these other churches.