I also would have said "Sikh" and "seek" are homonyms until recently when I found out that Sikhs' preferred pronunciation is generally to sound closer to "sick" (aspirate the H if you like)
I'm going to listen out for how Sikhs pronounce it.
I've heard "Sikh" pronounced many times by native english speakers and that invariably sounds like "seek". Now that I've heard that it's pronounced differently by the Sikhs themselves, I'll aim to use the correct pronunciation. This is an unusual situation in that I am a "native" (i.e. a native of England) and arguably Sikhs are non-native though I'd expect most of them near us were born here.
Also, the English have a long history of turning up in other countries and pushing their own religion/language/culture onto the natives, so maybe I'm just a product of my upbringing?
It feels similar to the situation with "Muslim" or "islam", which have a proper "s" sound in Arabic (as in "messy") rather than a "z" sound (as in "music").
Suppose the people of Edinburgh didn't happen to like Ee-dan-borghh as the French say it, that doesn't make the French pronunciation "wrong".