While stationary, putting full load on a single tire is probably OK. Only time I have seen a problem is on a triple axle unit where the owner drove the front tire up on blocks to change the middle tire. So that was a 3X load and the front tire then failed 100 miles later.
If you have a blow out and drive any distance with the other tire overloaded, then you should consider changing both tires. Also, flying debris from the failed tire can damage the other tire anyway, like causing internal tread separation. I had a case where the steel cord from the failed tire became imbedded in the other tire tread (didn't fail luckily). If you do replace both tires, then you should also rotate tires so both new tires are on the same axle.
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Larry Day, Texas Baptist Men volunteer
'13 Silverado LT 3500HD D/A CCSB 2wd, custom RKI bed
'19 Starcraft Telluride 292RLS
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