what do you use instead of date pickers?

I'd have to type in the date manually which is pita.

Separate fields formatted in ISO8601 format?

It all depends on your use case, dropdowns are a nightmare to get right as setting the dropdown for months influences the amount of options in the dropdown for days. Same goes for years.

If you're asking a user to input a birthdate it doesn't really make sense to show a date picker, as the actual day and week doesn't really matter, also, each and everyone of us have our birthdates memorized as a set of numbers, so offering separate input fields allows for quicker input.

I mostly test if <input type="date"/> is supported, if so, leave it alone (the device will show a date picker). Else, offer input fields based on the options described above.