Did your AC freeze up? If not and the evaporator coil is clean there is not any consequence.
A plugged filter reduces the airflow and may allow liquid refrigerant to reach the compressor. The primary danger with a plugged filter or evaporator coil is to the compressor. Some compressors are more vulnerable to damage than others, More expensive ac designs have all sort of components and design features to protect the compressor, the cheap builders grade systems do not.
Dirty filters reduce the capacity and efficiency of your AC system. They can increase your electrical bill.
To put your situation in perspective, I've seen filters that were so filthy they looked like cardboard and the system frozen, still running and working when the filters were replaced..
I've also had broken compressors that were on systems with similar filters and had the evap plugged with dirt.
Typically in badly neglected systems with filters that were years old.
“I am for doing good to the poor, but...I think the best way of doing good to the poor, is not making them easy in poverty, but leading or driving them out of it. I observed...that the more public provisions were made for the poor, the less they provided for themselves, and of course became poorer. And, on the contrary, the less was done for them, the more they did for themselves, and became richer.”
― Benjamin Franklin
I normally replace the filters faithfully every month but just forgot this month. I am running in heat mode. The system is an Amer. Std. Heritage 15 with a recip. Compressor with low and high pressure sensors as well as a TAM 7 Hyperion air handler.
2 months is the less important factor, how did the filter look when you pulled it out? I get customers all the time that leave the filter 90 days because that's what the "rated life" is, regardless of how bad they look.
Regarding the time before a filter change is required; that varies a lot depending on how much time the furnace was operating & the level of lint & other debris cycling into the filter.
Additionally, a one inch fiber glass filter needs a low velocity of airflow passing through it; anything above 500-fpm will cause excessive debris to pass through that media filter.
According to ACCA Manual D the filter area ought to be sized so there is 300-fpm airflow through a clean filter; it is very rare to have that sizing for either the heating or A/C mode.
The formulas are: say, 1200-CFM required for both the heating & cooling modes; 1200-CFM / 300-fpm is 4-sf of free-air-area or, Ak.
Figuring free-area; using Hart&Cooley Engineering tables: for 1309-CFM it takes a 30 x 30 filter 6.25-sf area with an (Ak) free-air-area of 4.363-sf, for an initial 300-fpm velocity.
The 4.363 / 6.25 is .70% or, a 30% loss of (Ak) net free-air-area, which is what counts toward velocity.
As the filter loads the sf of Ak is reduced & the airflow velocity will increase until it surpasses the 500-fpm velocity limit through a cheap fiber glass filter.
Regardless of whether you're using cheaper lower velocity media types or, one inch deep pleated type filters, - in many situations there is a need for two RA filter areas in the conditioned areas or, in two RA streams of the RA ductwork.
If you are concerned about more efficient filtering & keeping the evaporator coil clean, you might consider adding another equally sized or even larger filtering area.
What are the highest CFM requirements of your heating & cooling modes; plus the size of the existing filtering area?
The Filter is in the furnace; in the ductwork or, in the conditioned area?
I dont think forgetting to change a filter one time for a month will cause any issues. Dont worry, just get into the habit of checking often, and if you have pets, check more often. Ive seen homes with a couple of cats and dogs inside that needed filter changes a few times a month, depending of breeds.
Just depends on how dirty it is and how much margin you have for error... ie how large the filter is compared to hte maximum CFM required. A 20x25 on a 2 ton system will last a lot longer than on a 3 ton system. A 5" media filter on a 2 ton system might last a year, but only 6 months on a 4 ro 5 ton system.
I'm spoiled and just rely on my Infinity system to tell me when it's dirty since it monitors static pressure change over time.