If anyone really wants to support a theory that Democrats are actually the reason why the measure passed, I think the math doesn't really add up. Polling puts the number of people who identify as "Republicans" at 46%. Democrats are 31%. Independents/unaffiliated are 23%.Here you go.
State Primary Election Types
The manner in which party primary elections are conducted varies widely from state to state. Primaries can be categorized as either closed, partially closed, partially open, open to unaffiliated voters, open or top-two.www.ncsl.org
This site classifies Kansas as "open to unaffiliated voters". Just to muddy the waters up a bit...
n.b.: Indiana is "partially open" according to this site.
Almost half of registered voters turned out, which is pretty heavy for a primary election. It doesn't look like Republicans stayed home. And if they did, they're obviously more casual about their views on abortion than one might expect. But I don't see much support for the idea that Democrats outperformed their distribution by enough to have made the difference.
I think anti-abortionists need to accept that the results of Kansas likely reflected the will of the voters, including Republican voters. And though I haven't seen statistics on it, I suspect that a majority of the people who identify as Republicans who voted nay on the referendum were women.