Is the usage of this ‘to permit this’ ungrammatical in this sentence from the Economist?

Solution 1:

To infinitives can be used in a number of ways. I would say that you've mistaken the way that "to permit this" is used in this sentence (which is not extremely clearly written, but which I think is grammatical).

Pressure will therefore mount for vaccinated people to be able to move around freely, even if at first they will be too few in number to make much difference to the economy. If governments ignore calls for “vaccine passports” to permit this, the vaccinated are likely to change their behaviour regardless.

In this sentence, I would interpret "to permit this" as meaning something like "in order to permit the free motion of vaccinated people". One use of the to infinitive is to describe a purpose; in this sense, to can often be replaced with the longer paraphrase "in order to".

The to infinitive here is being attached to “vaccine passports” in order to explain the purpose the passports would serve.

Compare it to the use of "to allow a degree of normality to return" in the following sentence:

Faced with deep recession, governments around the world are considering the use of immunity passports to allow a degree of normality to return.

("What is an immunity passport and could it work?", World Economic Forum, 19 Jun 2020, Charlotte Edmond)

Here the infinitive phrase introduced by to is attached either to "immunity passports" or "(the) use of immunity passports".

In contrast, in a sentence like "...calls for the minister to resign", the to infinitive "to resign" cannot be paraphrased as "in order to resign". Rather, the verb in the to infinitive here describes the action that is being called for, with "the minister" functioning as the logical subject of the infinitive. This construction can be paraphrased as "...calls for the minister's resignation".

Solution 2:

The preceding sentence is vital context:

'Pressure will therefore mount for vaccinated people to be able to move around freely, even if at first they will be too few in number to make much difference to the economy. If governments ignore calls for “vaccine passports” to permit this, the vaccinated are likely to change their behaviour regardless.'

'This' thus refers to 'for vaccinated people to be able to move around freely'. Vaccine passports would allow them to do so.