I had my current engineered wood floor installed over concrete about 19 years ago. I have had no moisture related issues and the floor installation has held up well other than wear/tear. Long story short, I am replacing it with a new engineered wood floor (3/8") in Houston, TX. Is it necessary to test the slab for moisture if the prior floor did not have any moisture issues? There is a significant variance in cost for adhesives that provide moisture protection so my second questions would be, if there is no evidence of moisture on the current floors is it safe to go with an adhesive that does not provide that protection and which one would you recommend.

Thank you in advance for your suggestions.

No - the slab would not need to be re-tested after such a long period of time without issues.

I also would agree that the moisture protection built into some adhesives is not necessary for this case. Those products tend to be good for installs over crawlspaces or below grade applications where moisture may occur.

Thank you for your prompt response. Is Bostik MultiGrip Urethane Wood Flooring Adhesive a decent product for my application?

Older wood adhesives were less prone to moisture intrusion. Play it safe and use an adhesive that blocks 100% of the moisture like Sika T-21, Bostik Greenforce etc. Some adhesives are only good to 85%.
Also make sure all the old adhesive residue is off the slab.