inhibition of H2 receptors: (for GERD) prevent gastric acid secretion (cimetidine,
inhibition of phosphodiesterases (PDE):
β2 agonists: (for asthma) cause bronchodilation
(idk lymphocyte membrane stabilization)
While antihistamines with action at H1 receptors are used for allergies, H2 antihistamines are typically used for ulcers. Therefore the best answer is stabilization of mast cell membranes. These drugs (cromolyn) prevent vesicles of histamine from fusing with the membrane.
The unnamed drug class in question are the cromoglycates, the two most notable being cromoyln and nedocromil