The phrase "shameful act" means doing something that is morally wrong, embarrassing, or dishonorable. It refers to an action or behavior that causes feelings of guilt, regret, or disgrace. Full definition
For their women exchanged their natural function for an unnatural and abnormal one, 27 And the men also turned from natural relations with women and were set ablaze (burning out, consumed) with lust for one another — men committing shameful acts with men and suffering in their own bodies and personalities the inevitable consequences and penalty of their wrong - doing and going astray, which was [their] fitting retribution. (redeeminggod.com)
As you keep reading down to verse 26 it states that GOD GAVE THEM UP TO DISHONORABLE PASSIONS and Paul goes into detail of these dishonorable passions stating that women changed their natural relations for relations that go against nature and that the men likewise gave up their natural relations with the women and were consumed with passion for one another, men committing shameful acts with men. (religion.blogs.cnn.com)
For this reason is why GOD ALLOWED humanity to do shameful acts. (religion.blogs.cnn.com)