@Yep... Thank you for asking this question, it is great to hear fellow birders being thoughtful of their surroundings, fellow people, and limiting your impact on those. Of course, any real birder knows that respect for our environments, property and other people is central to birding anyways. Here's my take, for what it's worth. (Sadly, my trip to Peele is also off the table
)
I live next to an urban park, and have been grateful that we have been allowed to continue using it safely as possible. I own a beagle, and without the off-leash areas, its next to impossible to get her tired out, and an ornery beagle at home is enough to drive you crazy. So I've been taking her for an hour or two each day, and taking binocs with me. She has been surprisingly quick to join in my erratic and sudden stops for any flighty movements. I have been sticking to side trails, not only are they better for birds, I rarely run into anyone. I must admit, my own mental and physical health is greatly benefiting from this activity too, and feel I am avoiding most risks, considering my dog and I do need the exercise anyways.
That said.... I'm not driving there. And it's practical enough to avoid the main entrance and scarcely encounter people. I am having a difficult time convincing myself I could simply drive 10min to Humber Bay Park. Take side streets and go slow? Sure. Go on a non-sunny/ even -drizzly day? Sure, actually good for the incoming songbirds (?!) and less people out there. But obviously it is far from essential. Can I combine the trip with picking up some take out form a local business, and getting groceries? Seems unwise actually. Best to stick to my usual grocery store, with same people, and same germs.
I'm clearly torn, and not really helping decide anything here. I think a short, low speed car trip to a less-used park on an off-day is something I would consider doing. Driving across the Gardiner to join the flocks of people on a sunny Sunday at Humber Bay though, I think would be a 'No'. I imagine most birders would avoid that anyways on a normal year, let alone with the current COVID situation. Like you've said, there not really any parking anyways, and there's small risks with driving that we don't need to take. But I'm in a 1 bedroom unit, with no job (read:purpose) right now, and an introverted need to spend time without my (lovely) spouse. I think I feel OK with taking the odd trip, once or twice a month, to a less-than-local park on an off day. Especially if I were in a position where I was further from a park. Personally I think I will stick to my local park because I am extremely lucky, but I would be understanding of those who need to take a trip, as safely as possible.
TL;DR If done as safe and sparingly as possible, a short trip to a park has tremendous health benefits, and I think should be OK for those in need of doing so.