Instead of using 1s and 0s you can just use 1,2,3,4,... next to the cells you want to alternate.
Then paste the exact same sequence under underneath (like this)
1
2
3
4
1
2
3
4

Then just with the data filter (like in the original example) just sort by ascending or descending and you will have blank rows

(Credit to my friend Angus)

I just get the first line of the data I'm copying filling all the rows. Tried using 'skip blanks' but it doesn't work.

It only works if you copy a single cell, which pretty is useless. For a range of data it doesn't work.

Thanks. Works with Google Sheets (April 2020). Use formula =MOD(ROW(),2) to create the alternating pattern.

The cell you create your filter in gets turned into a header, so you want to select the cell ABOVE your range and in the data menu choose create filter. It should auto-detect your number range and add a filter. Or you could just highlight your whole range (+ 1 cell above it) beforehand.

Click the little filter icon that appears in the header cell to adjust settings of what to display.

When done you can then copy paste your result into another program if needed.

didnt work for me either

shows alternate rows but when i paste, it pastes normal way, doesnt skip cells.

It doesn't work

This doesn't work for me. I have Microsoft Office 2010, so whichever version of excel comes with that I am not quite sure but either way it doesn't work. When I paste it pastes to ALL rows. So, when I paste I only see half of what I pasted, when I turn the filter off I see everything I pasted =/