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Hello Vance,
Certainly! It is completely possible for a sentence to be grammatical according to one speaker and ungrammatical according to another.
In many areas of grammar there is complete agreement, so, almost all native English speakers would find something like *"He ringed the bell" ungrammatical.
However, there are also many areas, especially when it comes to more advanced grammar and usage where there is still debate, even among the experts. For example, "I need to quickly find somewhere to stay" is something that many native speakers may find acceptable, while others would argue that you can never put any other words between "to" and the verb in an infinitive.
Another classic example: "Who is it?" - "It's me." vs "Who is it?" - "It is I." Most native speakers would use the first one; purists would argue that the second one is correct... (There is no object in the sentence, so an object pronoun like "me" should not be used.) I could go on, but I'm sure you've heard enough already...