OK to mix - Bias Ply fronts w/ Drag Radials?

I run radials on the front and Hoosier Quick Time DOT's on the rear which are bias ply...this is for dragstrip use only.
I've done street radial and bias plys on front ans slicks and drags on back

I've could not perceive a difference but I've been told its not a good idea

For me it was more of what did I have that fit at the time also some of the radial skinnys (I think) have poor top speed ratings. I a told for 1/4 mile speed rating is not as important for front as its not a sustained speed so less tim to overheat???
if it was as unsafe as some people make it out to be, the NHRA, IHRA, and every other drag racing sanctioning body wouldn't allow you to mix bias and radial tires on the same car.
I run my car like that and I dont think it really matters what the construction is if you have skinnies up front.