While Kesha Rogers without question holds positions on many issues that are sharply at odds with those of most Democrats, she has the right to profess to be a Democrat and run for public office as a Democrat, something she has in fact done during the past three election cycles, serving as the Democratic nominee in CD-22 in 2010 and 2012 after defeating Democratic primary opponents.
In the United States in general, and in Texas in particular, anyone can claim to be a Democrat or Republican and compete in that party's primary, even if they hold positions that are anathema to an overwhelming majority of people that identify with and support the party.
Thus, just as Louisiana Republicans two dozen years ago could not prevent former KKK Grand Wizard David Duke from publicly identifying himself as a Republican and running for office as a Republican, Texas Democrats can not prevent Kesha Rogers from publicly identifying as a Democrat and running in the Democratic primary.
If Hinojosa is claiming that he does not consider Rogers to be a Democrat, that would be accurate. Assuming that is his opinion, which I assume is the case.
If Hinojosa is claiming that Rogers holds positions that are inconsistent with those held by most Democrats, that would also be accurate.
If however Chairman Hinojosa is claiming that Rogers is not a Democrat, that would be inaccurate. She publicly identifies as a Democrat and has for the past three electoral cycles run as a candidate in the Democratic Party, serving as the party's CD-22 candidate in 2010 and 2012. While she is clearly in a fringe faction within the Democratic Party, a faction with longstanding roots in the party whose views on many (though not all) major issues are clearly far outside of the Democratic mainstream, her self-identification and political participation are consistently Democratic.
She also ran for TDP Chair in 2006 if I'm not mistaken.
And, in the end, in Texas the chairs of the TDP and RPT do not have the authority to decide who is a Democrat or Republican respectively, and who is not.