Wrong: If someone is not of the same opinion as the others wanting this safe space (yet of a skin colour or some other requirement that entitles them access to the safe space), they're under no obligation to use it.
No, they're not. What judgement is going on here? Furthermore, where's the "stereotyping"?
If some white people want to put forward an argument for giving them safe space from whatever then by all means let them do so, however if they're going to try and argue that they need safe space from non-whites based on some argument with substance as opposed to some knee-jerk "they've got safe space, I want one too" reaction.
Lots of things go on in society that have requirements that (on the face of them) perhaps shouldn't be required. For example, I was listening to BBC Radio 4 on the way home, talking about a survey of British Muslims that has made the news recently. It was said that Muslim researchers were sent out to knock on doors of British Muslims and survey them. Shock horror! That sounds like discrimination to me! Should that honestly be allowed? Couldn't a non-Muslim person do a job like this perfectly well? Yes, very likely. However, if you have a minority that you wish to survey, would you consider it wise to send out someone like me (white, male, shaven head) to survey them? Do you think that someone who is part of a minority is going to respond as well to someone who fits stereotypical criteria of someone who might shove poo through their letterbox or throw a brick through their window?
On the other hand, if you were surveying white people, such considerations are not so important because chances are that they haven't experienced unwarranted prejudicial hostility/marginalisation.