At the OF Mass no-one makes any gestures when the processional cross passes or the priest for either procession.
At the EF Mass as I sit towards the front, I don’t know what the rest of the congregation does, though I suspect just from those around me, the majority do nothing.
I have noticed one lady cross herself and I think bow her head when the processional cross passes during the entrance and she, myself and another couple bow slightly from the waist when the priest passes during both entrance and exit processions. (I usually have my head buried in the hymnal and singing so don’t notice the processional crucifix until after it’s passed by, so I don’t cross myself at these times.)