Praise be to Allah.
The answer to this question is based on the definition of what is meant by doing the actions of wudoo’ consecutively and whether that is a condition of wudoo’ being valid.
Those who say that doing the actions consecutively is a condition of wudoo’ being valid differed concerning what exactly is meant by doing them consecutively, and the length of the interruption that could render invalid what the individual has already done of wudoo’.
The Hanbalis (may Allah have mercy on them) were of the view that what is meant by doing the actions of wudoo’ consecutively is that the individual should not delay washing any part for so long that the part that was washed before it becomes dry, within an average timespan.
Al-Mirdaawi (may Allah have mercy on him) said in al-Insaaf (1/141) regarding doing the actions of wudoo’ consecutively: It means not delaying the washing of any part for so long that the part that was washed before it becomes dry. What is meant is: within an average timespan.
This is the view of the madhhab, and it is the view of the majority of our companions.
The second view is that doing the actions of wudoo’ consecutively is to be based on custom. So whatever is customarily regarded as too long of an interruption is the interruption that breaks the consecutive sequence, and whatever is customarily regarded as not being too long of an interruption is does not affect the consecutive sequence. This view was narrated from Imam Ahmad (may Allah have mercy on him).
The author of al-Insaaf (1/141) said: And it was narrated from him – meaning Imam Ahmad – that the length of the interruption is to be based on custom. End quote.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: One of the scholars said – and it was narrated from Ahmad – that with regard to the interruption, what matters is what is customarily regarded as a lengthy interruption, not the drying of limbs, because the parts of the body must be washed soon after one another. So if the people say that this man did not separate the actions of wudoo’, rather he did it continuously, then he is regarded as having done the actions consecutively. The scholars took custom and tradition into consideration regarding many issues.
But it may be difficult to define the timespan on the basis of custom, so connecting the ruling to the drying of limbs is a clearer definition." (Ash-Sharh al-Mumti‘ 1/193).
What is mentioned in the question of simply opening the door and the like is not regarded as an interruption that would nullify doing the actions consecutively, regardless of whether we follow the first or second view in defining the time that is regarded as nullifying doing the actions consecutively. That is because opening the door usually takes only a short time, then the individual may resume his wudoo’ without any of the limbs that he has already washed becoming dry.
But if he is distracted by something else that leads to a lengthy interruption, then in this case he should start his wudoo’ anew.
And Allah knows best.