I can't really see parks opening again until the situation has normalized completely, whenever that may be. Issuing masks to everybody isn't likely to become an option until masks are produced in abundant numbers for everybody, and currently they are pretty scarce (luckily, almost every country up there is starting up production lines, so give it a few months). But even when masks are as available as toilet paper, there's still the issue of wearing them correctly, and that tends to clash with how parks operate. For instance, they need to be properly disposed of, not just stuffed into any ol' trash bin around the park. There needs to be extra masks available whenever a new one is needed, so the park would have to supply them by the bucketload. Parks also earn quite a bit of revenue on food and drinks, and that's incompatible with proper mask use. Sure, you could wash your hands and mouth and sanitize and put on a new mask afterwards, so it's not impossible to eat or drink per se. But regardless, it's pretty likely that you would buy less stuff than you would have otherwise.
There are other factors as well. I'd bet most parks don't have the facilities available for everyone to wash their hands as often and as thoroughly as is recommended - which requires a lot of sinks, soap and hot water all over the park, more than is already required for toilets. People would also have to stand far apart in ride queues, which absolutely tanks their capacity with a risk of spillover into midways - which then become too crowded for crowds to move through them. Virtual queuing gives the same problem, as many park midways are built around the assumption that a large fraction of guests will be standing in queue lines at any given time. Take people out of the queues, and then everybody will be in the midways, congesting them beyond the safe levels. Of course, this could be mitigated by letting fewer people into the park in the first place, but then the question remains if there would be enough guests for the park to run a profit - especially considering the extra cost of operation under those circumstances.
And again, as touched upon previously in the thread: How fun would it be to go to a park with such measures in place? Having to wear masks, maintaining a distance to people and washing hands frequently is fine for adults, but if you're a parent who wants to take three kids to a park, it becomes a major hassle to ensure that everyone is complying at all times. Wait times for rides would be atrocious as they'd operate with fewer available seats and needing a good wipe down every so many ride cycles. Food and drinks would be another hassle. And there's also the action of going out among people in the first place. There is a clear risk associated with it, a perception of danger even though the measures would reduce it significantly. Would enough people consider the risk worth it to bother going to a park? I think it wouldn't be profitable to operate a park until normalcy is restored, and even then, it will take a while before people turn up in droves again. At any rate, 2020 is probably a total write-off for most seasonal parks.