In the 1840s the Republic of Texas had about 70.000 people while there were about 30.000 Mormons. If all or most of the Mormons relocated to Texas they'd soon outnumber the other settlers so I wouldn't see them being chased out, especially since prior to his death Smith had gotten approval from Sam Houston to settle Mormons in Texas
If Texas and the mexican government reacts to Mormons the way the bulk of the US reacted to them the idea of outnumbering the Texans is not gonna be a major factor for long. The Mormons have an entire culture based around how much oppression they faced int he founding of the church.
Now said oppression is linked to marriage practices, religious doctrine, but also the political impact of tens of thousands of "radicals" appearing in a community. Nauvoo for example had 12-15,000 in 1844 making it almost the same population as the city of Chicago. However locals would not put up with such a place and a mixture of attacks, isolation, and economic blockade made the mormons have to flee the region.
Cause if we speak of the Mormons reaching Texas then it means it is when the church was fleeing persecution, and that Joesph Smith was in power. So this is either pre-June 1844 or the mob in the jail never kill Smith but chase him off. Now for Young it took almost a year to reach Utah, Texas may be mildly faster given routes at the time. However if we say they arrive in 1845 or 1846 this puts them in the center of Texas issues.
Likewise even in 1844 the LDS church was dealing with the fallout from the Kirtland Safety Society collapse. Which made non-Mormons view banks run by mormons as proto-ponzi schemes.
Then using OTL do we see the Utah War transplanted into Texas? Smith is either alive, or Young is in charge so the small cadre of Mormon settlers who hinted at forming an independent state will certainly be present.
Plus now I think of it with the Mormons in Texas there is a greater form of resentment linked to "popular soverignty" the go to notion to support slavery. Mormons used similar terms to defend plural marriage. I mean in 1856 the GOP openly said they wanted to end "polygamy and slavery."
So to me sending Mormons to a place where people were more then eager to fight supposed threats to their way of life, alongside under the control of Mexico would only end in hardship. Polygamy is a major hot button issue, and even under the cloak of religion it does nothing to defend the Mormon church. Salt Lake was in the middle of nowhere, and let settlers going to California and Oregon gain supplies and sell goods the Mormons demanded. It was a nexus point for a "alterantive" faith to take root and settle down.