Good question.
In reality it doesn't really, no more than Lewis owning us defines us.
But, and it's a huge but, the perception of the club by others would be different.
Being owned by an autocratic regime that thinks it's ok to discriminate against large portions of society will have an effect on some fans.
I'm talking in general here, rather than just Spurs.
For example;
Were we to be owned by Pol Pot (extreme, I know) would people be saying " Nah it's fine, I don't care about the @ 2 million innocent people killed under his regime. It doesn't change what Spurs are"
I highly doubt it.
Edit:
There has to be a line somewhere, although it's fine for people to have different views on where that line is.