Is it possible to be blocked access to a free public park/playground? ?

Yes, the police can ask you leave.  In my state, ALL parks are closed.  

In my community, we have small playgrounds dispersed throughout the town, for kids under age 12 with slides, swings, jungle gyms, and rocking animals the little children can ride.  

Since the lock down they removed the swings and put police tape across the stationary equipment, even the park benches are taped so you can't sit there.  

They posted a sign that the park is closed until the Covid lock down is over.  Everyone is abiding this order and the parks remain empty. 

The grassy area surrounding the playgrounds are not taped off, so I suppose you could play catch or some other game with your child there, but I haven't seen anyone doing that since the lock down.

Emergency powers give elected officials the right to close such places. Some have taken this to extremes. The people bucking these orders and posting their arrests online often represent not average citizens but organized Libertarian groups. In the most severe cases a rational person could rightly say that both sides are wrong.

Your city made that decision and passed an ordinance which they are within their rights to do in the extraordinary circumstances of Covid-19. The police did not make that decision on their own, they were following orders like thousands of other towns and cities across the country. Playground equipment that kids climb and play on has been identified as being exceptionally dangerous for transmitting the virus from one kid to another.

Yes, the police can order them to leave and arrest them if they don't comply, which is what happened. Stepping on our Constitutional rights seems quite reasonable to many people in authority during this pandemic.

Yes, it is. Park was closed. So that makes them trespassing.

The local PD can demand a group of people leave a public park.  That public park actually belongs to and is cared for by some government...probably the City in this case.  And for cities, the PD's are the enforcers.  So if the City sees that distancing and such are being violated on the playground, but not the open park area, they can certainly cause their PD to clear the playground.

Don't you see the difference between a playground with rides and slides, and an open park land?  I'll spell it out for you.

The difference is those rides and slides.  Your kids are touching them and leaving whatever virus they might have on them.  And your neighbor's kids are also touching them and picking up whatever virus your kids left for them.  Now both your kids and theirs go home where they pass on the viruses they picked up to you and your folks if they happen to be living with you and to your best friends who live next door with their parents.

Note, I didn't even mention that your kids and theirs are likely to touch each other as they play on and around those slides and rides.

Please don't be a part of the problem.

"can the police legally ask/tell the parents to leave public property?"

Of course.   People are blocked access to public property every single day.    It's not like you can go to your local library at 2 AM or go apply for a building permit on a Sunday.

Just because a facility is taxpayer funded doesn't mean the public is entitled to 24/7 access.   Facilities have hours of operation and also close for other reasons such as maintenance, safety issues, off-season, etc.

Certainly.... but keep in mind many of these "freak out videos" are distributed by the same people who show videos of the very same cops in the very same parks "freaking out" and "going all Gestapo" on skateboarders and weed smokers...

...more often than not, the point is not to inform or promote informed discussion...but rather to encourage feelings that can then be manipulated to promote a particular agenda....

in some cities, the playgrounds have been closed