I agree. This seems like a prime example of a base rate fallacy.

If all 4 transgender candidates ran afoul of this law, and none of the cisgender candidates did, it's reasonable to think that it might be an anti-trans law. But, that ignores the base rate of name changes. Probably about 1% of non-trans people change their names, or use names different from their official names when submitting paperwork to get onto a ballot other than women who take a married name -- but there's an explicit carve-out for that because it's so common. Probably about 99% of trans people change their names or use different names in that same situation. The rate of name changes between the two groups is massively different, so one group is going to encounter the issue much, much more often.

In the past, when trans people simply didn't try to run for office, this wouldn't come up very often, so nobody paid much attention to the badly designed forms, etc. But, now a new group of people is starting to run for office, and this group encounters the problem nearly 100% of the time.

And, while it's also possible to think this might be an old law that's now being weaponized by the other party against trans people, the article shows that they can't do that:

Earlier this month, the board received a protest to Childrey’s ballot certification from Mercer County Republican Party Chairman Robert J. Hibner. Because the ballot is for the upcoming March 19 primary, the board ruled Hibner’s protest invalid, as Hibner is from the opposing political party.

There may still be prejudice at play, that trans candidates are under more scrutiny than a white cis male who wanted to go by Jimbo and not James. But, IMO incompetence / bugs in the system is probably a bigger part of the problem.