I have run with unmatched tyres many times. Other than the initial difference in how the bike feels when you go from a worn tyre to a new tyre, i would challenge any normal rider to be able to tell the difference between tyres from different brands, if you were to conduct a blind test. The fact that we are involved in the tyre selection process after probably reading dozens of posts and video's giving views good and bad towards any brand or specific tyre, we maybe aren't best placed to give a totally unbiased assessment of a tyre's performance or characteristics. I mean, i cant even tell the difference in how the bike handles when i've filled it up with fuel, and i dont ride like a granny, but a top level racer i am not.
So my main point is this.
If you took your bike in to the tyre shop, and asked them to swap the front from a michelin to a conti, then got on and rode the bike, would you know? would it throw you over the first hedge to came to? no. Do tyre manufacturers want you to fit matched pairs, throwing away part worn tyres? yes.
As long as the two tyres are of the same type ie sport touring, sport, then you aren't going to have any problem.
We do this on cars all the time, without a second thought, i know cars a different, but i bet tyre and car companies would recommend all 4 tyre were the same.
I also challenge your point that tyres are the one thing that keeps you alive, riding within your, and the bike's abilities and the road's limitations tend to be what keeps you alive, not the brand moulded into the sidewall of your tyre.
Just my view of coarse
Stu