Well, Pol in DAII still has no blood writing on his face when we meet him(at least 4 years after he joined the tribe), but Lanaya does have blood writing on her face.
And according to Lanaya, she suffered quite a bid of prejudiced when she joined the tribe and became a candidate to be the tribe's First, but she says this is due to her lack of 'pure blood', rather than any religious disagreements, as Lanaya likely converted when she was brought to the clan.
Pol might not be ready. The elven pantheon is tied with the vallaslin, according to what Keeper Gishrael wrote, "The ritual deserves great reverence. The one who is to gain the vallaslin must prepare by meditating on the gods and the ways of our people, and by purifying the body and the skin. When the time comes, the keeper of the clan applies the blood writing. This is done in complete silence. Cries of pain are signs of weakness. If one cannot tolerate the pain of the blood writing, they are not ready to undertake the responsibilities of an adult. The keeper may stop the ritual if they decide that the one gaining the vallaslin is not ready. There is no shame in this, for all children are different, and our ancestors once took centuries to come of age."
Lanaya mentions not originally being Dalish was an issue when she competed against several others for the role of First, but she also says that the mistrust faded away in time, as Zathrian said it would. Lanaya also mentions wanting to stay with the clan when Zathrian rescued her from the human bandits who murdered her parents and enslaved her. I suspect, after what she endured, she welcomed a life among the People.
I'm of the opinion that the Dalish clans are all very different from one another in a variety of respects. Some of them probably place greater importance on religion than others. But I think that in order to become a part of the tribe, conversion is probably a need of social necessity to the new tribe memeber as much as anything else. Afterall, the Dalish are not the most welcoming people in general. There's probably an expectation that in order to become one of them, religious conversion is simply a natural part of the process.
To be fair, the Dalish are wary of outsiders because they have historically been a threat to them since they had an independent kingdom, and they still have to deal with human lords or lynch mobs running them off the land if they remain too long. It's a defense mechanism that's kept them alive for centuries. And I'd imagine that wanting to join the Dalish would mean wanting to become Dalish, and all that would entail, especially given the importance of the vallaslin. Gisharel wrote, "When the children of our people came of age, they earn the privilege of wearing the vallaslin, the blood writing. It sets us apart from the shemlen, and from the elves who have thrown their lot in with them. It reminds us that we will never again surrender our traditions and beliefs."