> Tangent: Protestantism is not a religion. The religion is called Christianity. I have seen this trend for quite a while of Protestants (or people born in Protestant countries) of referring to Christianity branches as religions.
Deciding what is a “branch” of a religion versus whats is an independent “religion” is more subjective than objective. This might become clearer if we move away from Christianity for a moment, and look at the same question for some non-Christian religions
Consider the southern Indian religious movement of Ayyavazhi - most people, both in India and outside it, consider it a branch/denomination/sect of Hinduism, including even many followers of Ayyavazhi - but some of its followers and leaders insist it is a separate Dharmic religion [0]. The question is (in part) political - Dravidian nationalists and Tamil nationalists are more likely to call it a separate religion, Indian nationalists (Congress) and Hindu nationalists (BJP) want to view it as part of Hinduism
Meanwhile, most people consider Buddhism, Jainism and Sikhism to be separate religions from Hinduism - but the British courts in India decided they were branches of Hinduism, a classification still followed by the Indian legal system to this day. Many Hindu nationalists promote the idea that these traditions are branches of Hinduism, even though most of the Indian followers of those religions reject the idea.
It is standard to classify the Alevis in Turkey as an Islamic sect - yet the Turkish government wants to insist on the idea they aren’t even a sect, just a “cultural movement”, to promote the fiction of a homogeneous Turkish Islam - but while some Alevis are fighting for government recognition as a separate sect of Islam, there is a movement among Alevis (Ishikism) which claims it is a separate pre-Islamic religion, and its Islamic content is just a superficial distraction (dissimulation) to prevent persecution. Meanwhile, many hardline Sunnis around the world agree that Alevis are a non-Islamic religion - and some of the most hardline Sunnis will even say that of mainstream Twelver Shi’a.
So, the boundary between “branch of a religion” and “separate independent religion” is more subjective (theological and political) than objective.
[0] https://m.economictimes.com/news/elections/lok-sabha/tamil-n...