Late today, Governor Abbott announced the third phase of reopening businesses, allowing virtually all businesses to open immediately at 50% capacity.
Restaurants, already allowed to operate at 50% capacity, will no be allowed to increase table size from 6 to 10, and can operate at 75% capacity beginning June 12th.  Bars can immediately increase their capacity from 25% to 50%, but all customers must continue to be seated while in the establishments.  
There are also protocols for the opening of amusement parks and carnivals, phasing in the opening of these activities depending on the number of positive cases in a county.  All amusement parks and carnivals can begin to operate at 50% capacity by June 19th.  
The 50% limit now will no longer apply to personal care businesses such as hair and nail salons, massage studios, tanning salons, and barber shops as long as the work stations are at least 6 feet apart.
Below is a brief summary of the new protocols taken directly from the Governor’s press release sent out late this afternoon:  
And the executive order issued today can be found here:  https://gov.texas.gov/uploads/files/press/EO-GA-26_expanded_opening_COVID-19.pdf

Effective June 3:

All businesses currently operating at 25% capacity can expand their occupancy to 50% with certain exceptions. 

Bars and similar establishments may increase their capacity to 50% as long as patrons are seated.

Amusement parks and carnivals in counties with less than 1,000 confirmed positive cases may open at 50% capacity. 

Restaurants may expand their maximum table size from 6 to 10 persons.  

Effective June 12:

Restaurants may expand their occupancy levels to 75%. 

Counties with 10 or less active COVID-19 cases may expand their occupancy limits to 75%. Counties that fit this category but have not previously filed an attestation with DSHS will need to do so.

Effective June 19:

Amusement parks and carnivals in counties with more than 1,000 confirmed positive cases of COVID-19 may open at 50% capacity.

Additional Openings:

Special provisions have been made for outdoor gatherings, such as Fourth of July celebrations, but it is imperative that local officials and public health officials collaborate on safe standards. These provisions are included in the Governor’s Executive Order and are also available on the Open Texas webpage. 

Further Protocols:

All businesses should continue to follow the minimum standard health protocols from DSHS. For details and a full list of guidelines, openings, and relevant dates, visit http://open.texas.gov.

Reminders for those going out:

  • Individuals are encouraged to wear appropriate face coverings.
  • People should not be in groups greater than ten when possible.
  • People over the age of 65 are encouraged to stay at home as much as possible.
  • People are still asked to avoid nursing homes, state supported living centers, assisted living facilities, or long-term care facilities.