A321
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Workload; Time Pressure
Aircraft Equipment Problem Less Severe; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor
Air Traffic Control Provided Assistance; Flight Crew Overcame Equipment Problem; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Returned To Departure Airport; General Flight Cancelled / Delayed; General Maintenance Action
Aircraft
A321 TOGA (takeoff/go-around switch) takeoff with APU on. Pouring rain. While climbing through approx 18;000 ft; first one; then other flight attendants called to say they smelled a burning rubber smell in cabin but could not see smoke. Passengers were also complaining. We smelled deice fluid in cockpit (plane had flown from ZZZ1 to ZZZ); but otherwise we kept talking with them to see if it would dissipate. While still discussing a return to ZZZ; first one; then two passengers had trouble breathing and the flight attendants made a PA for a doctor on board. At this point we felt we needed to return to ZZZ for an overweight landing. We notified and coordinated with ATC; Dispatch; and ZZZ OPS to return and have paramedics at the gate. The cause was unknown; but aircraft did have an MEL for avionics cooling extract fan that required it to remain in override. Perhaps this could have contributed to burning smell or a different load on air conditioning.
The Captain (CA) and I noticed a smell in the flight deck while in the climb; roughly around 10;000 feet.  The FAs (flight attendants) called climbing through flight level 180 stating they smell an odor in the cabin.  The FAs also stated some passengers were complaining about the odor.   The Captain requested the flight attendants to call back in 10 minutes and state if the smell is dissipating.  The FAs call back shortly stating several passengers are having difficulty breathing.  At that time the Captain made the decision to return to the ZZZ.  I took over as Pilot Flying and ATC communications. I requested to return to the ZZZ and notified ATC for an overweight landing.  At that time the aircraft weighed roughly 180;000 lbs.  The CA took over Pilot Flying on the arrival shortly before joining the approach to runway.  The aircraft weighed approximately 177;000 lbs on landing.  When we arrived at the gate paramedics attended to several passengers who were having difficulties breathing. [Possible cause or related issue]; we were relatively heavy; had a slight tailwind and the runway was wet.  The TPS (takeoff performance system) called for config 2; TOGO; APU OFF.  As a measure of safety the CA decided to leave the APU and APU bleeds on.  I concurred.  The aircraft's extract fan was also MEL'd (MEL 21-05a).  The CA and I both felt the odor mostly resembled anti-icing fluid.  Though we also discussed the possibly the inoperative extract fan or the APU usage on takeoff was the cause of the odor.  But mostly we thought it was anti-icing fluid.  Once we realized passengers and the cabin crew were being affected the decision was made to return to ZZZ which resulted in an overweight landing.
A321 flight crew reported a fumes event during climb resulting in a return to the departure airport.