My approach, like Mike's, is not to hold taps in the tailstock chuck directly. Instead the chuck holds a spring loaded end piece that only keeps the tap straight. No pressure is put on the tailstock chuck in either direction.
As pictures are worth a 1000 words.

Small taps usually come with a male end while bigger taps are female, so two spring loaded tap-holders may be needed. I bought a male holder and made the female myself. Nothing complicated: a plunger working against a small coil spring inside a straight tube small enough to fit in the tailstocks drill-chuck. I used the spring out of an old biro pen.

Set up to cut a thread with a normal tap handle.

Starting with the tailstock pushed to fully compress the spring, I cut threads by holding the handle still while turning the chuck to and fro by hand. The tailstock is keeps alignment and is only moved if the spring doesn't have enough travel.
Not a good idea to cut threads under power with this arrangement. Apart from the danger of getting caught in the works, it's important to break and clear swarf by regularly reversing the tap by half a turn or so.
Dave