In veg, 60% is a good number, assuming that you keep temperature within a certain range. There are a lot of sites that give ballpark temperature and RH numbers and they'll work OK. If you're in flower and your RH is really high, that will impact that quality of your harvest. Similarly, if you raise seedlings in really low humidity, they won't grow as well as if you were raising them in high temps and high humidity.
When it's high temps and high humidity, humans call it "muggy" or "sticky" and we feel "clammy". That's the "feels like" temperature in a weather forecast. Plants are similar.
For each stage of a plants' growth, there's a range of temperature and humidity readings where a plant will photosynthesize at an optimal rate. As a seedling, hot and humid; for veg, moderation is the key; and for flower, keep temps < 80 and keep RH in the 50's or lower.
Those temperature and RH combinations can be expressed as "vapor pressure deficit" ("VPD"). Hit this link on the Pulse web site more information about VPD. They've got a slew of well written documents that explain VPD.
There are a lot of charts floating around the web that show you what combinations to use in the various plant growth stages and a few companies make sensors that help you keep plants at the right VPD. I use a PulseOne sensor but there's at least one other company that sells a sensor that's used with VPD and AC Infinity sells controllers for there fans that read temp and RH and calculate VPD.
Back to your question - you can put a plant in a tent that's got really high RH and growth will slow and you might end up with mildew but you'd have to work really hard at it to kill a plant with too much RH.