My site my rules. It’s pretty clear yes.
Of course I can't arbitrarily declare the laws of the country I operate in (or in the case of GDPR - the laws of the country my visitors are from) to be null and void. That's not what I was saying at all.
I was referring to those people who claim that my approach to moderation is not democratic - or that I'm restricting their "freedom of speech", thus showing a complete lack of understanding about what those things actually mean.
The government under whose jurisdiction I operate, sets the laws around what is acceptable - I cannot go beyond that. But within that broad range, I can set whatever rules I like.
I run my sites as a benevolent dictator - I set the rules, I interpret the rules to determine which content is acceptable and which isn't - and I enforce the rules strictly. If I go too far, people will leave. I need to find the balance between maintaining order and encouraging contribution - so I do try very hard to not be a **** about the rules.
For example, I run a fairly strict "no NSFW content" rule, I also ban discussion about certain topics and certain activities such as advertising or self promotion are strictly controlled.
To have someone complain that their freedom of speech is being supressed by my rules banning discussion about certain topics shows their fundamental misunderstanding about what freedom of speech actually is.
To declare my approach to moderation to not be democratic shows their fundamental minsunderstanding about what democracy actually is.
In the same vein - someone demanding that I remove all of their content posted on my forum as their "personal data" under GDPR laws shows their fundamental misunderstanding about what the GDPR laws actually say.