Your statement referred to 'race mixing' which is quite another thing altogether.
It's entirely possible to be 'offended' by the total destruction of one's culture and not so much by any inherent 'race mixing' that may be the result of that.
But yes - multiculturalism will definitely 'destroy' any culture wherein it is implemented - white/black/red or brown. That's a simple fact.
'Diversity' in the world is destroyed with multiculturalism. You get a 'rainbow of skin colours and last names' - sure - but you get a narrowing of culture and ideals. You get the lowest common denominator - not 'multiple viewpoints'.
You don't get 'more ideas' - you get 'officially sanctioned ideals'.
'Cultures' need 'critical mass' to exist, and they cannot be defined by GDP or social policy. Once there are too many cultures, or culturally secular ideals - the 'local culture' is completely abolished.
When you have 'diversity' in a locale - you break down cultural bonds - and replace them with material products - like Starbucks and McDonald's - and culturally secular values.
Example: I was in Tunisia recently, I drank a 'Tunisian tea' (what I called it). It was dirt cheap. The Coca-Cola was 2x more expensive. Paradox: selling 'coca cola' is essentially better for the GDP - 2x more dollars changing hands. Culturally secular politicians and economists will see this 'GDP growth' and push hard on it across all consumer and business sectors. New shopping malls with H&M, Zara, Starbucks, Monoprix, Carrefour etc. etc. - are literally up-ending all of the unique culture of some parts of that country.
After a while, 'Tunis', 'Toronto' and 'Singapore' will be the same place: same secular laws, same products, same services, same clothes, possibly speaking English, working in cubicles, driving the same cars back and forth.
All unique cultural artifacts - and there are many of them - abolished.
Tunisia is a very strange place to me - and that's what makes it great. I'm not looking forward to going back in 25 years when it's all been wiped out by globalism.
'Multiculturalism' is really just a very short transition period between 'culture' (i.e. diversity in the world) and 'globalized, culturally secular nation states'.
America (and Canada) are obviously special places where multicultural identity means something different than say Germany or Tunisia, nevertheless, the conversation should be allowed to had.
We already have a great deal of 'diversity' on planet earth, just get on an airplane! Most attempts to create 'more diversity' in a specific local (usually with the benign objective of wanting people to 'get along better') , actually reduces the 'net diversity' of the world, ironically.