Is arachnophobia connected to lower immunity against spider toxins?
This is an interesting question and may stem from the fact that spider phobias tend to run in families and thus have a genetic link - assuming susceptibility to toxin levels can be passed from parent to offspring.  However, instead a study found that the fear of spiders was caused by social learning of disgust reactions.  

Source: https://www.psychologytoday.com/blog/why-we-worry/201407/why-are-we-afraid-spiders

Directly from source:


  In relation to the first question, it has been known for many years
  that spider phobia tends to run in families. It has often been assumed
  that this may represent a biological predisposition caused by the
  transmission of genes between parents and offspring. However, we found
  that this relationship was considerably more complex and indirect. We
  found that the only significant predictor of a child’s spider fear was
  not the level of spider fear in the parents, but their levels of
  disgust sensitivity. One interpretation of this finding is that spider
  fear may be transmitted within families as the result of social
  learning of the nature and intensity of disgust reactions–including
  disgust reactions to spiders.


Link to study abstract: http://www.sciencedirect.com/science/article/pii/000579679390041R