RAW Forcing open a door is a Strength Check
Comparing Strength with Strength (Athletics) as described in the PHB, we can conclude that forcing open a door should be a Strength check.
Let’s start with Strength checks. The PHB says (175/176 – emphasis mine) says
A Strength check can model any attempt to lift, push, pull, or break something, to force your body through a space, or to otherwise apply brute force to a situation…
The DM might also call for a Strength check when you try to accomplish tasks like
• Force open a stuck, locked, or barred door
• Break free of bonds
• Push through a tunnel that is too small
• Hang on to a wagon while being dragged behind it
• Tip over a statue
• Keep a boulder from rolling
We note first that Strength checks are explicitly called out as being used for forcing doors open, as well as breaking things in general. On a more subtle note, we can see that they reflect short bursts of ‘brute force’, single events that either succeed or fail immediately.
On Strength (Athletics) checks, however, the PHB (175 – emphasis mine) says:
The Athletics skill reflects aptitude in certain kinds of Strength checks…Your Strength (Athletics) check covers difficult situations you encounter while climbing, jumping, or swimming. Examples include the following activities:
• You attempt to climb a sheer or slippery cliff, avoid hazards while scaling a wall, or cling to a surface while something is trying to knock you off.
• You try to jump an unusually long distance or pull off a stunt midjump.
• You struggle to swim or stay afloat in treacherous currents, storm-tossed waves, or areas of thick seaweed. Or another creature tries to push or pull you underwater
or otherwise interfere with your swimming.
By their nature, Athletics checks are not used for events, but rather for situations. There is some complex process that you are attempting over a period of time, and the DM calls for a check to see if you can pass the most difficult or dangerous part of the process. (Grammarians should note the shift from the simple tense descriptions of Strength checks to the progressive tenses of the Strength (Athletics) checks.)
Two people with equal Strengths might be equally good at the “burst strength” required to tip over a statue. But, by virtue of their Athletic training, a person with the Athletics skill would have the stamina, focus, balance, and determination needed for a long climb up a sheer cliff that someone with untrained raw strength would lack.
Applying this background understanding to the specific question of opening doors, we can assume that most doors would be subject to a single instance of burst strength, a single event of applying enough force to break through their structural integrity (lock, latch, bar, hinges, or what have you). A portcullis has a certain weight – if the character can lift the weight in a single burst (Strength), the portcullis can be lifted.
But there are situations in which Athletics could rightly be considered
A Strength (Athletics) check might be properly called for when opening the door or lifting the portcullis is no longer an event but has become a prolonged and difficult situation. For example – the gate of the palisade is thick and barred from the other side, and no simple burst of strength will sunder it. You can eventually chop through it with your axe, but can you do that before the orcs arrive?
You can lift the portcullis; you are strong enough for that, but can you hold it open for several rounds while the rest of the party makes it under and you are being subjected to missile and spell fire?