Re: During the rishta process…
With the lies and deceit going on these days and stories one hears or witnesses or god forbid ends up being a victim of …I wouldn’t blame anyone for requiring that either tbh! 
Re: During the rishta process...
While in theory it sounds okay (I'd have no problem with it as long as its a blood test) and I don't think anyone would mind a blood test.
But anything further than that I don't think that would go down too well.
But like Huma said, whatever floats anyone's boat!
Re: During the rishta process...
Also IMO if a rishta starts from such mistrust ie stuff beyond a medical test etc then the very foundation of that relationship is based on mistrust.
Blood testing is fine though imho.