Usually, the only time you can get into trouble is if the bullet you are switching to is larger in diameter, or the bearing surface is significantly longer than the original bullet the load was worked up with.
Many years ago, I acquired a bag of 30 cal, 150 grain Remington Kor-Lokt bullets. Threw my micrometer on a couple, they were .3082". I thought....good to go with a load I was using with the 150 Speer FBSP at the time.
Loaded up a box of 20 and headed to the range. First four were perfect, no pressure signs, all clustered in a group of just over 1 moa. 5th shot showed signs of pressure, bolt lift slightly sticky, and a mark from the ejector hole on the casehead.
I'm thinking: "What is going on here, did I perchance overcharge a case?
Gingerly, I chambered and fired another....it was just like the first 4, no pressure signs, all is well. So went the next 6 shots. Then, another round displayed pressure signs. Not serious, but enough to get my attention.
Took the rest home, [7 unfired rounds] and pulled them down. Powder charge was good, no other reasons apparent.
I decided to measure the bullets again. 6 of the remaining 7 were .3082, like the ones I had initially measured, but one was .3093", more than one thousandth larger. Curious, I dumped out that bag of bullets and started measuring.
There was obviously two different lots of bullets in there, with about ¼ of them being of the larger diameter. They appeared identical to the naked eye, but the micrometer told the truth.
Had this been a mild load, I would probably have never noticed. [except possibly on the target], but since it was a reasonably stiff, but safe working load, the extra diameter put it into the noticeable pressure area.
Always be careful. Surprises occasionally lurk out there.
Regards, Dave.