My parents have to move from Colorado to Texas so that I can take care of them, will Medicaid transfer and can I rent their house out?

Pam is right , medicaid aside, rent and upkeep of a house in another state is a pain. You will need to hire a property manager if you go that route. Liquidating assets and spending them on your parents needs is appropriate. You will have some relocation expenses for them, and yes, you will need to use the money for their care in the spend down, but chances are at least one of them will outlive assets. Are their funeral expenses paid for? There are numerous legitimate and practical ways to spend down assets.

Medicaid rules are very strict in Texas. You need to google Medicaid Information for Texas residents. My aunt is in the nursing home in Texas, yet owns a home in another city in Texas. If she were to rent it out, she would lose her Medicaid, as the rental money would be additional income. So tread lightly and contact Medicaid. Veterans might get some disability..Contact VA.....

No Medicaid will require all assets to be spent down, and I don't recommend trying to rent a house when you are in another state. If they are on Medicaid in Colorado, and they move out, there's a good chance the state will seize the property. Property is exempt only as long as you live there.
Texas may impose a waiting period before they allow them to apply for Medicaid, since they are not residents, and funding is limited. Lots of postings have complained about a long wait in Texas.
Your other option is to get home care for them where they are, and if Dad is a wartime veteran, the VA will help pay for it.