I did a most informal survey on r/saturatedfat, a very very highly selected sample of people who believe in the no-PUFA cause:
https://www.reddit.com/r/SaturatedFat/comments/1ebvtmx/call_for_anecdotes_how_long_does_the_sunburn/
The great majority of responders who actually answered the question, eleven people, said that they'd become sunburn-proof somewhere between 3 and 9 months after giving up all PUFAs.
One person reported that they had eventually become sunburn proof, but that it had taken four years.
And one luckless person reported that despite four years of not touching a PUFA, they still got sunburn.
There were also six 'spoiled ballots', five of whom reported various degrees of sunburn-tolerance and PUFA avoidance, and one I just couldn't understand.
I wouldn't take this too seriously, but on the other hand it does seem like if you forswear all polyunsaturated evil then you can probably expect to stop worrying about sunburn the following Summer.