Mexican citizens who lived in and owned property in Mexican Texas were not robbed of their property in the Republic of Texas or subsequently in American Texas - as long as they acknowledged the sovereignty of the Republic and then of the USA over the territory and abided by its laws.
I'm not sure who "we" is - if "we" is the federal government of the USA, you must surely realize that at least some of the land in Texas is privately owned.
What kind of conservative makes a statement like that?
Texas is a sovereign state within the Union. No one owns 'Texas'. The Texas people are sovereign and they Texas Republic never confiscated any Texas-Mexican private held land as a result of gaining their independence.