The way you worded your question opens the door to illegally aliens voting at some point in time.
Only in the imagination of someone who is full of fear.
So let's go through it...
Should eligible citizens be allowed to vote?
It's yes or no, really. They should. Period.
If yes, should states intentionally remove them from the rolls without reason?
No, they should not. Why would anyone disagree. If they have reason, then go for it.
At the "challenge" of complete strangers who know nothing about the voter whose right to vote they "challenge"?
This is crazy. Frankly, I hope a rogue group of liberals start doing this to conservatives just to prove a point and I hope those who support it have to suffer the consequences and can't vote. That's poetic justice.
Should states put up barriers to citizens voting or make it as easy as reasonably possible for as many people to vote as are eligible?
Why put up barriers to citizens voting? Why not make it as easy as reasonably possible for people who are eligible to vote?
There's not a single thing here that would help people ineligible to vote to be able to vote. Not a thing.