(1) is different in meaning from (2). (1) allows for the practice of letting some in but not others, as well as the practice of excluding all. It is standard English.
It is equivalent to 'I started refusing entry' (which again does not differentiate between selective refusal and total refusal).
I feel sure the introduction applies to both.
However, the introduction is ambiguous: 'letting them in' could mean all comers, or a selection, are being admitted.
It seems to me that, when all comers are being stopped, 'I stopped letting them in' is more likely to be used; and that when a selection only are being stopped, 'I started not to let them in' is much more likely.
It depends who 'them' refers to. That depends on the context. For example:
'I had been told to use my discretion when the crowd got too big. By nine o'clock, I felt I had to keep out the noisier elements. I had been letting them in before and then I started not to let them in. However, some then became angry because they had been kept out while others were still being admitted'.
The expression 'started not to let them in' may seem awkward, but it does seem to me to chime with the idea of selection in this suggested context.