I've used a number over the years. Currently back on Textra, which has never given me any trouble, including background usage (far less than some Samsung services that I have disabled every aspect of that it will allow me to). Prior to that I used QKSMS for a year or so, but there was one specific task it couldn't do (can't even remember exactly what) and after having to switch SMS app a couple of times I decided to just use Textra for a while.
But also what do you mean by "secure"? Actual SMS security is what it is independent of the app. Other types of messaging may be more secure, but need the other party to use the same app. And of course any app you give access to your contacts requires you trust the developer (so I will not recommend stuff like Go SMS because that company have proven that they can't be trusted in the past).