Blepharitis: This condition is characterized by inflammation of the eyelids, often accompanied by purulent discharge and erythema. The absence of pain and vision changes, along with the presence of purulent drainage, makes blepharitis a strong candidate, as it can be caused by bacterial infection (staphylococcal blepharitis) or other factors like seborrheic blepharitis.

Conjunctivitis: This is an inflammation or infection of the outer membrane of the eyeball and the inner eyelid. It can cause redness, itching, and discharge, which may be purulent in bacterial conjunctivitis. The symptoms can overlap with those described, making it a plausible diagnosis.
Hordeolum (Stye): A hordeolum is an acute, localized infection or inflammation of the eyelid margin involving hair follicles of the eyelashes (external hordeolum) or meibomian glands (internal hordeolum). While it typically presents with pain, some cases might have minimal discomfort, especially if the infection is mild or in its early stages.
Chalazion: This is a small bump on the eyelid due to a blocked oil gland. Although it's usually painless and doesn't typically cause purulent drainage, in some cases, a chalazion can become infected, leading to increased redness and possible discharge.

Orbital Cellulitis: This is an infection of the soft tissues surrounding the eye, which can lead to serious complications, including vision loss and cavernous sinus thrombosis. While the question mentions no pain or change in vision, early stages of orbital cellulitis might present subtly, and any sign of eyelid swelling with erythema and purulent discharge warrants consideration of this diagnosis due to its potential severity.
Endophthalmitis: Although this condition (inflammation of the interior of the eye, usually caused by infection) typically presents with severe eye pain and vision changes, atypical presentations can occur, especially in the early stages or in patients with compromised immune systems.

Erythema Multiforme: A skin condition characterized by target lesions, which can sometimes affect the eyes, leading to conjunctivitis and eyelid swelling. It's less likely given the specific symptoms but could be considered in the differential diagnosis due to its potential for ocular involvement.
Angioedema: This condition involves deep tissue swelling, which can affect the eyelids. While it's more commonly associated with allergic reactions and can cause significant discomfort, it's a rare consideration in this context unless there's a clear allergic component or other systemic symptoms.