Yes. Whether or not you support a union in any public or private way is up to you. It is illegal for management to grill anyone about union activity or to threaten, harass, or discriminate against anyone because of union activity. Workers attempting to form a union have legal rights and protections under the National Labor Relations Act.
Your employer cannot legally punish or discriminate against any worker because of union activity. For example:
Your employer cannot threaten to fire, lay off, discipline, harass, transfer, or reassign employees because they support the union
Your employer cannot favor employees who don't support the union over those who do in promotions, job assignments, wages, hours, enforcement of rules, or any other working condition
Your employer cannot shut down the work site or take away any benefits or privileges employees already enjoy in order to discourage union activity
Your employer cannot promise employees a pay increase, promotion, benefit, or special favor if they oppose the union.
If your employer violates the law, the union can help you file "Unfair Labor Practice" charges with the National Labor Relations Board.
Backed up by the federal courts, the Labor Board has the power to order an employer to stop interfering with employees' rights, to provide back pay, and to reverse any action taken against workers for union activity.