Character name: Kylee.

I took the zombies quest <snip>... Then became wanted and the questgiver stopped reacting.

Then I went to <second quest> and he gave me the quest. <snip>... but just like the Emissary, he did not react.

I wonder if I did something wrong, is it by design that both questgivers don't let you complete quest if wanted. <snip>

Thanks.

Regarding the first quest, the logs show you having successfully completed the quest on 09/13/16 (there is a limit on the number of bounties you can collect).

I don't see any record of you having even started the other quest, so there isn't much to work with there.