The easy answer for replacing the crew of the ISS is that your process will 'pass' about as many as there are current Astronauts simple because you do not need that many and will just add filters until your candidate pool meets the number of spots even if the final criteria is number of vowels in their name or similar.
if we are looking at making random people astronauts we get to the question of risk. Currently there is a surplus of astronauts so they can be multi trained, so any of them can command a return to earth, take care of injuries or fix life support systems. If we relax that requirement, for example by making them all fly as 'spam in a can' to orbit with no manual control and then have an expert on the ground meat puppeting them via headphones and camera we get lots more candidates but increase our risks by hard to quantify amounts when things go wrong.
What we can do is look at things that would rule people out.
There are currently size restrictions borne of capsule size (cannot be big) and seating arrangements (cannot have short legs). These are engineering/cost problems that can be solved with money if there was a reason to do so. This is assuming the only space suit they get is a rescue ball.
These studies seem to suggest that the majority of vaguely healthy people can survive the G-forces of a ride to orbit, and out of a sample size of two even pacemakers will not rule people out.
Space sickness is a problem with the majority of people seeming to suffer from it to some extent, though it appears nobody who has flown has required a mission abort from it, though there is a self selection element here. There are probably a small number of people who would dehydrate or starve due nausea, assuming similar numbers to sea sickness that would be under 1%.
A more ambiguous criteria is psychological. Somewhere between 8 and 2% of the population are concerned enough by flying commercially to either not fly or medicate themselves to fly, approximately matching these numbers for a simulated flight in a centrifuge. given the claustrophobia etc of space flight the numbers should be expected to be higher. Noting the number that reported medicating via alcohol this may be a complication for astronaut selection - is it ok if they need to be drunk to get into the capsule?
In terms of the skills required, the majority of people who can afford to seek a private pilots license seem to pass the academic components given enough time, suggesting that most people when sufficiently motivated can learn a combination of new to them mechanical and theory skills to at least that extant. This also suggests the ability for most people to learn some non intuitive muscle memory survival skills (eg stall recovery) with enough practice and exposure.
This skill question is important, since as anybody who has taught someone to drive learns humans have a strong tendency to freeze when faced with complex decisions and while this is useful when say choosing the non poisonous fruit, in many hypothetical space situations freezing up is lethal. Training helps but there is a strong normal distribution to 'function under pressure' and the related avoidance of inattention blindness that current astronaut selection process gets to pick the top performers at and a more general selection system would just have to accept changes to design to 'idiot proof' things and accept that this design (eg removing manual overrides) and human nature would kill a hard to quantify number of people.
In terms of surviving the environment of cramped living conditions, limited freedoms and constrained food, most people who enter the prison system survive. Suggesting that most humans can adapt and not die in conditions not unlike the ISS, albeit with a range of long term effects due stress and related conditions.
Taken together that suggests that if you have no ethics probably at least 50% of the adult population could be turned into an astronaut and not have them die straight away, the question is why this would be a good idea?
