A lot of singers stay away from vocal training lest the training change the inherent quality of their voice. This is a valid fear.
If you do not want to sing like an opera singer, but you want to learn how to sing healthily, and all that is available is operatic or classical vocal training, you have two choices. Go to the classical teacher and try to apply what you learn to other styles on your own or don’t study and try to teach yourself to sing in a way that sounds good and feels good, too. Most people are in one of these two categories if they haven’t given up!
Why should it be necessary to be in this dilemma? Why do I have to learn to make “operatic resonance” and sing foreign language art songs if I want to sing rock music or gospel songs? What has one thing to do with the other?
Further, if you are a classical singer, you might be afraid to sing anything that isn’t your “classical sound” lest you hurt your voice or mess up that technique you worked so hard to develop. Also a valid fear. You could do either or both. Or not.
Being afraid to make any sound, lest you disturb the one you like or need, is absolutely not necessary, if (and only if) you study with someone who knows what has to happen to sing classically and also not sing classically and do both well. Good luck finding such teachers. They are very rare.
Vocal function is not the same as “classical training”. You can train the voice to be free, healthy, and versatile, as well as appropriate to both your body and your desired style(s) if you know how to do that. Learning classical vocal production and repertoire is completely unnecessary. You can learn to sound like yourself, only better. You can learn to make all sorts of sounds without being afraid. You can sing with freedom and control and like your sound. That, in fact, should be the purpose of training.
Be suspicious of teachers who have platitudes like “I don’t want any head voice (register, resonance, tones) on this pitch because it is gospel music”. This belies great ignorance. Question people who tell you that classical training is necessary if you want to sing well. Bad classical training is never necessary. Good classical training might help a rank beginner at least when starting out, but has to be adapted past that early stage. Excellent functional training can include classical vocal production if that is desired, but can leave it out and still cultivate a developed, well-coordinated vocal sound.
Fear isn’t supposed to be part of the learning process when it comes to singing. If you are afraid in your lessons or in your songs, something is W R O N G. Get better help.