Be open-minded, but never so open-minded that your brain falls out, you can't use critical thinking, or you don't have opinions of your own. Disliking something or believing it to be untrue never prevented anyone from living their life.
To people who aren't spiritual, the whole idea of otherkin is just unrealistic. To people who are, they may have their reasons for believing that something like a dragon being incarnated as a human isn't possible. Even when it comes to personal beliefs a degree of caution is needed, because some things are honestly spiritual and others are part of a sickness.
Many spiritual communities have the concept of something they call Unverified Personal Gnosis for dealing with the more unusual personal beliefs, especially those not shared by others or that contradict with more traditional sources of information. They want to be able to find out what's truly spiritual and what's just someone listening a little too much to the voices in their heads, that source of mostly-random noise and subconscious chatter that everyone has. The problem being, if you treat every whim as a message from the beyond and follow it to extremes you'll literally be in a fantasy world and may be putting yourself (or others) in danger.
One woman on a forum mentioned on a topic about interpreting messages from the beyond how, during a very sick period, she became convinced that the fetus of her dead child was telling her to harm herself in ritual repentance. While that's a very dark and extreme example, the fact holds that people can be seeing spiritual things and messages from the beyond that aren't real because they're sick. One woman might talk to her dead child, another might have been told by angels that he's actually a dragon. If these people are otherwise doing okay and these things happen, there's a different way to approach it and try to come to a conclusion about what to believe.
That's the gist of people's caution when it comes to these kinds of beliefs on a spiritual level. On a psychological one, it can be difficult to distinguish between something like maladaptive daydreaming, mental illness, or other problems and someone who is healthy but has an unusual identity or interpretation. The issue with people who gained an otherkin identity because of those reasons is that they tend not to be able to face that, and in my experience they tend to just be difficult to be around in general. You get all kinds of teenagers and even adults with anger issues towards humans and stuff like that, even when it's spiritual.
Oftentimes people who are on the mild end of a seriousness spectrum don't want to be mistaken for those on the extreme end, when extremes tend to stand out and be seen as "too weird".