The situation's still tense between the construction industry and the union representing its workers as a union organiser faces court this morning for trespass.

CFMEU rep Bill White was arrested at Fairbrother's Royal Hobart Hospital site last month after allegedly refusing a direction to leave.

Members have rallied outside the Magistrates Court this morning.

While Unions Tasmania claims Mr White was simply doing his job, Michael Kerschbaum from Master Builders Tasmania says they won't tolerate any bullying tactics from unions.