In 1908, the FBI was established. And guess who was the POTUS back in 1908? Theodore Roosevelt. He was a Republican. However to be fair, PBS described him as a moderate Progressive. This meant the FBI was established before the party switch.
But these days, the FBI haven't even locked up Trump and Hunter Biden was spared from jail by the skin of the teeth. Hunter was a lot closer to end up locked up than Trump because the FBI favour the Republicans. Always have, always will do
https://archives.fbi.gov/archives/fun-games/kids/history-of-the-fbi-text-version