I noticed while playing with different character builds that some skill's bonuses seem to get stuck no matter if you change the attribute or background boosting it. I don't know if the skill screen just isn't updating or if they're actually stuck like this. I first noticed it last night while deciding on a character build. I was trying to decide between two backgrounds based on the skills they gave me, and I was going back and forth on the backgrounds and swapping the INT and WIS attributes when all of the WIS based skills became stuck, no matter how I changed things around.
I ended up going to bed and was re-creating the character tonight. I had finally decided on the background and skills, but was tinkering with my attributes. When I finally settled on what I wanted, I checked the skill screen and noticed the performance and persuasion skills were stuck at +3, which is very odd because neither of those skills are in the background I picked, and I can't even select them due to my class. As you can see in the screen shot below, I dumped all attributes down to 8, and a bunch of skills are incorrect. The skills I'm getting proficiency bonuses in should be +1, and the rest should be -1. Notice all of the DEX skills are +1, Animal Handling is +1, the WIS skills are +1 or +3, and Performance and Persuasion are +3.