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People who follow Hinduism are classified based on varnas. If someone didn't follow Hinduism, how are their varnas determined ? If not, do they belong to any new category?

Consider a white man, what is his varna?

If you say it is based on their birth (in the current scenario), by which way do you classify them?

If it is based on occupation, then there is no clear way to do it (the father may be a governor, while the son may be merchant - which would make you give a different varna to father and son - which does not happen).

Also please mention a reference to vedas, mausmirthi or some book based on which you make a classification.

Their Varnas can not be known precisely. Simply because their races propagated without following the marriage rules prescribed in the Hindu scriptures. So, they may have had innumerable instances of what is called mixing of castes, speaking from the perspective of Hindu scriptures like Manu Smriti.

But originally they definitely had to belong to one of the 4 Varnas or the other. But due to the fact that they had stopped following the purificatory rituals (Upanayana and other Samskaras) they have attained the status of what is known in the scriptures as Vratyas.

Manu Smriti 10.42. By the power of austerities and of the seed (from
which they sprang), these (races) obtain here among men more exalted
or lower rank in successive births.

10.43. But in consequence of the omission of the sacred rites, and of their not consulting Brahmanas, the following tribes of Kshatriyas
have gradually sunk in this world to the condition of Sudras;

10.44. (Viz.) the Paundrakas, the Kodas, the Dravidas, the Kambogas, the Yavanas, the Sakas, the Paradas, the Pahlavas, the Chinas, the
Kiratas, and the Daradas.

So, for example, according to the above verses, Chinese, Greeks were originally Kshatriyas but they gradually became Vratyas.

And, Vratyas are not included in the 4-Varna system.

So, precisely knowing their Varnas now is an impossible task. Knowing which Varna their ancestors belonged to is equally an impossible task for us unless scriptures specify that for some particular tribes (like Manu Smriti did here for some tribes).

Now, there is also a group of people according to whom the Varnas are determined not by birth but by Gunas (personal traits). If that is the case answering your question (generally) isn't possible.

You have to investigate individually then. For example they also say if someone is into teaching then he is a Brahmin, a police/military person is a Kshatriya, a business man a Vaishya and one who does manual labour is a Sudra. So, if that is true you can check what kind of works a particular person does/likes to get his Varna. But this is not of course the traditional system. In this system there is no scope of any Samskaras.