No - all of those things about care workers not being paid to travel, about being fined by employers etc are terrible.
But they are not caused by climate change protestors.
They are caused by policy choices. It is the policy choice of successive governments to not pay carers appropriately, boost employment rights, require travel time to count, to not boost the minimum wage and not subsidise childcare, it is their choice not to lift universal credit. It's their choice not to help poor families insulate their homes to cut energy usage and reduce their bills.
It's their choice not invest in good bus services outside some cities, or to provide safe walking and cycling routes to allow people to safely and efficiently go to work, school, shop etc - all of which would reduce congestion for ambulances AND help reduce oil demand and energy usage
We can have a better world - for the climate, for care workers, for children, for ambulance drivers, for everyone.