Shots should be available to get the players vaccinated now, but I understand there is a fairly large number of MLB players are reluctant to get the vaccine.
I know that last week in Dallas, they had next day and even walk in spots available to receive COVID vaccinations. Every adult is eligible. Tarrant County (Fort Worth and Arlington) exhausted their 880,000 wait list more than a week ago. I have six grandchildren who have gotten their first shots and are awaiting their second. Four in Texas and two in New York.
In the past several days, I am seeing PSA ads on TV urging everyone to get vaccinated. Shots are available and every team should be able to be fully vaccinated by mid-May at the latest IF the players will accept the vaccine.