Overall I'd say my parents were fairly lenient for the most part when it came to food. If there was really something we didn't like or couldn't handle eating for the most part, they didn't force us just as long as the budget wasn't tight, and as long as we showed we would eat at least something.
I think it scored points in our favor that we've always loved steamed broccoli and potatoes. One thing my parents always marveled at was that my brother and I would actually eat our vegetables like a tasty treat, as long as it was done right, while other parents struggled just to get their kids to TOUCH their veggies, haha.
I guess there really are a lot of things that are kinda a generational thing, too. Mom has told me stories about how her family grew up poor. If she was eating at her grandmother's place, her grandma would just keep serving and serving and expect everyone to eat it all up, and would even be a little hurt if people stopped eating.
As for Mom's mother, that was a household with an extremely tight budget, and Mom's parents really were serious when they said that you either eat what was on the table that night, or you eat nothing. And a big part of that was because they literally could not afford to go out and buy you something else if you didn't like it. They were lucky to get the food that they'd already gotten.
Perhaps it's also for this reason that I grew up in a bit of a mixed atmosphere. Mom grew up in an environment where she and her sisters never, ever had to go without the basic essentials at least, but as a result, she is the most non-picky eater I've ever seen. Even to the point of not caring what gets mixed together, even if it's cauliflower and hot dogs sliced up into spaghetti.
Dad, on the other hand, is a lot pickier and he apparently can't even eat his vegetables if the bowl has a bit too much fluid in it, even if it's just melted butter. (He'll pour it off himself if it's too much.)
I guess in a lot of ways, we're pretty fortunate to be living in the age we're living in if we're picky, cuz for the most part food is plentiful (at least in my experience for the most part) and there's helpful services if you get into a budget crunch.