Your anecdotal experience is not borne out by either facts or my anecdotal experience.

Houston is literally the most diverse city in America, statistically speaking.

And you have to look hard to find religiously conservative people in any Texas metro that are also exclusionary. I say that as someone neither white nor Christian.

If anything, the only place you may find a lack of diversity is Austin, which is overwhelmingly white and overwhelmingly intolerant of non-leftist opinions.