Is it possible to have too many priors in Bayes Theorem? Each prior restricts the sample space, so in theory, your probability becomes more and more accurate. However, if our sample space becomes too small, the tradeoff between the accurate sample and the confidence we gain from having more data points becomes apparent.
Example: Assume I want to know the odds that I will contract COVID. I ask myself what is $P(\text{getting covid} | \text{20 years old})$. Let's say I get $10\%$. Then I stack another prior to get even more accurate data. I ask myself what is $P(\text{getting covid} | \text{20 years old} \land \text{is not obese})$. Great. Even more accurate probability.
However, what if I ask myself $P(\text{getting COVID} | \text{I have a tattoo of my name on my arm})$. Let's say there are $2$ people in the world, me and my friend, who have a tattoo of my name on his/her arm. Let's say my friend got COVID. This gives me a $1$ in $2$ odds of getting COVID which dosen't make sense.
A couple of ideas - maybe Bayes Theorem should be only used as a tool, maybe the priors have to be relevant to the outcome, maybe there's a threshold below which our sample is not significant. Not sure.

You are not asking about having too many priors, but about conditioning. The prior in Bayes theorem is this part
$$
p(A|B) = \frac{p(B|A) ~\overbrace{p(A)}^\text{prior}}{p(N)}
$$
while you seem to be asking about conditioning $p(B|\cdot)$ on many different variables. First, notice that conditional probabilities $p(B|A)$, $p(B|C)$, $p(B|C,A)$, $p(B|D,A)$, etc tell you about different scenarios. The probability that a CrossValidated.com user named Neel Sandell gets COVID is a different thing than the probability that any random person gets it, or that an MD working on a COVID ward gets it. Each time you condition, you restrict the space, that is correct. When you ask about probability given that someone has blond hair, the answer would be relevant only to the blond-haired people, not people in general. So you asked about a specific scenario, your question was restricted, not the answer.
This has nothing to do with the priors, it is just the bare fact that if you ask different questions, you get different answers, and if you ask specific questions, you get specific answers that may not be relevant to the general problem.
