[susan53]

Here the preposition has nothing to do with the noun day, but is dependent on participation :

You need in with all expressions related to the verb "participate" .

He was unwilling to participate in the demonstration.
Are you going to take part in the protest.
I expect your active participation in the lesson.

In your example you could change the end and the in would remain :

Union leaders called for the active participation of all members in the strike

showing that it depends on the noun participation, not on what follows.

So, in other words, here the prepositional phrase in the day of protest is the complement of of the verb, and not a time adverbial - as would be "on the day of the protest". Compare :

We are organising a strike. All members are expected to participate in the strike.
We are organising a day of protest.All members are expected to participate in the day of protest.

We are organising a strike on Thursday. All members are expected to participate on Thursday.
We are organising a protest The protest is on Thursday. All members are expected to participate on the day of the protest.


We are