Second the need more info thing.
One thing is that for sure is that if a GLO finds that a chapter has violated the GLO's non-discrimination policies (eg, rejecting an African-American on the basis of race alone), they can for sure yank the chapter's charter. But that can be really hard to prove. You can always say (as I have heard many say on this site) "Oh, Minority PNM just didn't mesh with our chapter." hmmmm.
It's also for sure that many national NIC and NPC GLOs did threaten to shut down chapters in the 60s because the chapters began accepting minority members. Sad but true.

I do not know if they actually did shut down chapters for this reason but I assume that there is at least one or two cases, perhaps quite a few, where this did happen.
I can't think of any NIC/NPC GLO that would allow discrimination on the basis of race anymore. I have heard that some groups may still allow some discrimination in terms of religion (eg, only Christians or more broadly in some cases, people who believe in a higher power, can join this group), but I've never heard of a chapter being dechartered for that. I have heard anecdotal stuff (which I don't know if it's true) about individual members have their membership revoked for such reasons. Mostly in NIC fraternities. Never heard about that with NPCs.
On the other hand, I have heard of some complex situations with Jewish NPCs where they are allowed to accept non-Jewish members (I believe all the traditionally Jewish NPCs accept non-Jews into membership) and being encouraged to accept non-Jews by their nationals for various reasons, and the chapter vehemently wanting to remain an all-Jewish group. That can obviously cause tension between the national and the local chapter, but I've never heard of it coming to a point of dechartering or anything like that.