You guys are going to see a lot from me. I have been reading here a lot the past few years, but now we have moved out of the neighborhood and have some property.
We have a 1 acre front yard that is nothing but grass. Full sun.
It also has the septic leach field right in the middle of it.
How close can/should we have any vegetable gardens near each leg? I can see where each line is due to the evenly spaced very green grass rows.

No real issues, human and animal waste is used as fertilizer around the world.  That said, I would only eat cooked goods.  Obviously, if you know of any chemical injection into your system, then you may or may not want to.

Only put shallow rooted vegetables close to leach lines.  There is a risk that the roots would interfere/penetrate the lines.

Who knows what chemicals have been poured down the drain and are in the soil. How many medicines where the previous owners on? Those get flushed out of the body through waste. Then you have the risk of plugging up the lines with roots. Do you have a water softener? Where does the brine discharge too?

Good questions.  Most contaminant will degrade between treatment and natural attenuation in the leachfield.  I'd consider the possibility of heavy metals concentrating and remaining stable.  So grow food that will not uptake these elements.  Most fruiting vegetables like tomatoes are not going to carry lead, arsenic, antimony (common heavy metals for those casting)  to the fruit.  The softening poses an interesting consideration.  In an arid area, it could possibly raise the soil salinity (never see it here as it leaches faster than accumulates), but also consider CEC softening swaps out +2 cations, so yo will get some mineral deposit too.

I personally would not raise root or leafy plants in the leachfield.

Good points. The brine is discharged to a separate ditch line.

So what would you guys consider a safe distance to plant from the lines? 10'? 50'?

I guess that would depend on the soil.