Sorry, I don't know what the right name is for this construction with "may" or I might find something that could explain it better. I'll try to explain it again, but I'm not sure if I can do it any more clearly. Maybe someone else knows what it's called.
In June 2020, Boris Johnson held parties at Downing Street.
At that time, most people were following the Covid rules such as not meeting more than 2 people indoors. Sie haben sich zu dem Zeitpunkt an die Regeln gehalten.
People are angry that perhaps the politicians were not following the rules in June 2020.
= People are angry that politicians may not have been following the rules in June 2020.
(Those last two sentences mean the same thing, dass sie sich eventuell zu dem Zeitpunkt nicht an die Regeln gehalten haben.)
The present perfect progressive e.g. "they have been following" is normally related to the present in some way. It means that the time you are describing is not finished now, or has only just finished now, in the present.
The past progressive e.g. "they were following" is not related to the present. It's talking about an activity that was in progress at a finished, historical time in the past.
When you add "may" to something in the past progressive, meaning "perhaps", it changes the form of the sentence so it looks like the present perfect progressive. But it's still talking about the past only; it isn't related to the present at all, and doesn't work like the present perfect progressive normally does.