I'm Black. Golliwogs are a racist caricature of Black peoples and are offensive.
In 2010 I saw those mugs on sale at a Blackpool market while on holiday. I was so shocked that I pointed and laughed at them loudly which embarrassed the market stall holder (she knew she was in the wrong!). I'm from London so had no idea there were corners of the country where they were still being openly sold.
I was on that holiday with my white husband's white 80 year old grandmother. She was confused by my shock as she had no idea that golliwogs were racist. To be honest, I didn't expect her to know. But here is the crucial bit: when I explained to my oblivious 80 year old, white, northern, low-educated, village dwelling, grandmother-in-law why they were racist, she LISTENED, took in what I was saying, PROCESSED the information and UNDERSTOOD. In contrast her grammar school educated, well travelled, baby boomer son (my FIL) put a golliwog on his Facebook page a few years later and didn't delete it when the offence was explained to him. So now I'm very low contact with him and he hardly sees his mixed race grandson.
The most offensive thing on this thread and in all conversations about golliwogs and other anti-POC things is that when the offensive nature is explained to white people they insist on telling you that you are wrong and that they, the white person knows much better about what is and isn't racist to a black person. What the fuck is that?!