If you’re burning the diesel within 8 hours after it was in a bucket for day 1 hour it’s not an issue. You shouldn’t store solvents in buckets that aren’t rated for solvents but you could carry that shit up the stairs in a paper to go box and it would still burn.
I don't have much experience with diesel but the wrong plastic with gasoline will turn it to jelly in minutes. I wouldn't consider it worth the risk to use random plastic buckets to carry fuel.