Are we more/less resistant to infectious diseases during an allergic reaction?
There are a number of issues with your question, and the short answer is no.

Immunity to pathogens is conferred by antibodies, but not usually of the IgE group. Pathogens usually stimulate IgM -> IgG; IgAs are present in mucosal surfaces.

There are multiple kinds of "allergic responses", and each carries its own risks.


  
  Type I reactions (ie, immediate hypersensitivity reactions) involve immunoglobulin E (IgE)–mediated release of histamine and other mediators from mast cells and basophils.  
  Type II reactions (ie, cytotoxic hypersensitivity reactions) involve immunoglobulin G or immunoglobulin M antibodies bound to cell surface antigens, with subsequent complement fixation.
  Type III reactions (ie, immune-complex reactions) involve circulating antigen-antibody immune complexes that deposit in postcapillary venules, with subsequent complement fixation.
  Type IV reactions (ie, delayed hypersensitivity reactions, cell-mediated immunity) are mediated by T cells rather than by antibodies. 
  


Limiting ourselves to allergic responses mediated by IgE, we have anaphylaxis, allergic asthma, urticaria, angioedema, allergic rhinitis, some types of drug reactions, and atopic dermatitis. These reactions can result in something as mild as urticaria or as life-threatening as anaphylaxis. None of these conditions carries an increased or decreased general immunological response to pathogens.

If allergy affected immunocompetency, one would expect to see, for example, an increased incidence of fungal infections in allergic individuals, but this is not the case. Allergy does not result in an immunocompromised condition, nor does it result in a primed response (an idea popular in the 90's). They are mediated by different pathways.

Effector mechanisms in allergic reactions
The production of IgE
Allergy, Parasites, and the Hygiene Hypothesis
Immunocompetence and allergy