It won't necessarily. In handgun cartridges it mainly depends on whether the space in the case can take the pressure of the extra gas made by a magnum primer without it unseating the bullet before the powder burn gets underway. Sometimes, when there is a lot of empty space in the case and the magnum primers are not unseating the bullets, they are actually better for accuracy by increasing start pressure. That's explained in the article I linked to in my earlier post.
Also, don't just change to a different primer without knocking the charge weight down another 5% and working back up. Ironically, under some circumstances a standard primer can cause higher pressure than a magnum primer does. This is mainly when the magnum primer is unseating the bullet but the standard one is not, so the powder fired by the standard primer starts building pressure in a smaller space.
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