I believe best practice is to have not only the same make, but exactly the same spec tyre on each axle - that is what I always do, anyway. I replace tyres in pairs.
And I've always shunned "part-worn" tyres.
I go further than than, I want them the same front and rear and with even wear. I move them around to achieve that and replace all four together.
If the car came with four identical tyres, it stands to reason you will change the balance unless you keep it that way. That might, or might not, matter but you won't know until it does.
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