No, probability is not "meaningless for singular events". We can meaningfully discuss, in Bayesian terms, the probability of drawing a red ball from a jar, even if that jar will be destroyed after the single draw. The probabilities are assessments about our state of knowledge.

Therefore no, we cannot dismiss all anthropic reasoning for the reasons you suggested.

If you got "probability is meaningless for singular events" from what you learned here, either you are confused, or I am. (Possibly both.)