Individual candidates who wish to run as Greens will have to pony up filing fees or collect a goodly number of signatures on a petition in order to run for elective office; the amount of dollars or signatures varies according to the office sought.
There's potential confusion in reading the record. The legislative history for HB 2504 says "Effective immediately," but that is merely an indication that the bill's status as statute takes effect immediately. The provisions of the bill itself go into effect on 1 September 2019, at which time the Texas Election Code will be officially modified.
I'll try to find out whether the effective date means that a prospective Green Party candidate must wait until September to begin collecting signatures; that doesn't appear to be the case, as there's nothing to stop a candidate from raising funds right now.
To be continued.