I'm not trying to change your mind. I'm simply presenting accurate information instead of propaganda.
I'm not sure of the origin of the whole "empty the mind" idea that people have regarding these practices. But it's a knee-jerk and inaccurate response. Perhaps it comes from the kind of syncretistic practice of some of these things during the 60s and 70s. Maybe it's a Transcendental Meditation thing (I'm not super-familiar with TM); however, it doesn't apply to yoga nor any of the kinds of meditation with which I'm familiar.
Pratyahara is not about "emptying the mind." For example, something that is very popular right not is "turning off the technology"--that is, taking one day a week, or a period of time to fast from technological devices. THIS would be an example of the practice of pratyahara. You are "withdrawing your senses." Some people will use a sensory deprivation chamber to relax in (this was popular in the 90s)...also pratyahara. Deliberately turning off all the noise in your home to appreciate silence...pratyahara. "Tuning out" ambient noise to concentrate on your project for work is pratyahara. NONE of this involves "emptying the mind."
Additionally, samadhi doesn't involve "emptying the mind." Here's a quote about samadhi: In the state of samadhi the body and senses are at rest, as if asleep, yet the faculty of mind and reason are alert, as if awake; one goes beyond consciousness.
If anything, samadhi involves a quieting of the BODY and the SENSES, not the mind. Now, clearly, the idea of samadhi is a concept based on a religious understanding of the human/divine relationship that is not Christian. Christians are part of Christ's Body when become His. However, even within the definition of this pagan idea, there is no concept of "emptying the mind."
Both your examples of Mindfulness and Concentration are also the OPPOSITE of emptying the mind. When you concentrate, you engage in a particular kind of focus. Concentration is good and necessary. You need to concentrate to be a good student in school. You need to concentrate to be a good lover to your spouse. You need to concentrate to be an attentive parent to your children.
And you need to concentrate when you pray to God.
Mindfulness involves becoming the observer of your own thinking. In other words, it's metacognition. A person needs to engage in metacognition to have any kind of self-control. "Wow, my mind is telling me to eat another cookie, but I observe that I'm not hungry. I will avoid that cookie." "Wow, I just got the impulse to punch my sister. Punching my sister would hurt her and get my into trouble. I need to not do it." Additionally, metacognition is necessary to engage in psychological change (renewing of the mind), to beat addiction, to understand how we learn best, and to engage in any kind of significant self-examination.
The fact that meditation helps people to concentrate AND to be mindful seem like good arguments FOR meditation, in my view of it.
Additionally, there is a long-standing history of meditative prayer within the Christian church.
Finally, I'm not advocating that anyone do anything....except speak ACCURATELY about these practices. I don't think we need to invent false stories about various practices in order to avoid them. If you cannot in good conscience practice yoga....then you ought not practice it.
I, however, can in good conscience practice yoga. So...I'm going to do so.