With practice you can learn to play where your finger isn’t against the open string that needs to ring.
Say I am play a roll on the first, second, and 5th strings (foggy mtn Brkdwn). If I need to fret the second string on the third fret I will place my fretting finger toward the third string enough so the first string will ring clear. this works for most things.
Another option is to take your banjo to a luthier and see if there is room on the neck to separate the strings a bit farther apart. this can be done at the nut, the bridge or both depending on what the player is looking for, but it will also cost some money.
Hope this helps. good Luck!