How to deal with people who try to prove your compassion is fake?

A Dhamma practitioner should be firm & unwavering in their conviction towards the efficacy of their virtue & compassion and remain untouched by criticism.

One should observe my example of being unmoving towards the cultural marxist politically correct opponents & subverters of Dhamma

How can that truly know the virtue of compassion humiliate others?

If their reproach is genuine with goodwill to correct your mistake you should contemplate on their reproach before you aim to respond. Contemplate on your compassionate acts weigh them against their reproach. Virtue is best seen in action!

After contemplating, If you still have a conviction that they are mistaken in their understanding of the virtue of compassion, and if they are asking to learn from you, then correct them.

If you know how to farm and feed your family what is there humiliating if someone says you don't know how to farm? What reason is there even to answer? Perhaps you may inquire how he/ she farm to learn new ways, but I don't see the humiliation.

This is the chance to cultivate and practise the brahmavihara of equanimity (upekkha), in addition to compassion (karuna).

From The Four Sublime States by Ven. Nyanaponika, where he discusses the relationship between equanimity and compassion:

Equanimity rooted in insight is the guiding and restraining power for the other three sublime states. It points out to them the direction they have to take, and sees to it that this direction is followed. Equanimity guards love and compassion from being dissipated in vain quests and from going astray in the labyrinths of uncontrolled emotion. Equanimity, being a vigilant self-control for the sake of the final goal, does not allow sympathetic joy to rest content with humble results, forgetting the real aims we have to strive for.

Equanimity, which means "even-mindedness," gives to love an even, unchanging firmness and loyalty. It endows it with the great virtue of patience. Equanimity furnishes compassion with an even, unwavering courage and fearlessness, enabling it to face the awesome abyss of misery and despair which confront boundless compassion again and again. To the active side of compassion, equanimity is the calm and firm hand led by wisdom — indispensable to those who want to practice the difficult art of helping others. And here again equanimity means patience, the patient devotion to the work of compassion.

How to practise equanimity?

Firstly, have confidence in your good deeds and intentions.

If, however, fear or uncertainty should arise, we know the refuge where it can be allayed: our good deeds (kamma-patisarana). By taking this refuge, confidence and courage will grow within us — confidence in the protecting power of our good deeds done in the past; courage to perform more good deeds right now, despite the discouraging hardships of our present life. For we know that noble and selfless deeds provide the best defense against the hard blows of destiny, that it is never too late but always the right time for good actions.

Secondly, let go association with the self:

The second insight on which equanimity should be based is the Buddha's teaching of no-self (anatta). This doctrine shows that in the ultimate sense deeds are not performed by any self, nor do their results affect any self. Further, it shows that if there is no self, we cannot speak of "my own." It is the delusion of a self that creates suffering and hinders or disturbs equanimity. If this or that quality of ours is blamed, one thinks: "I am blamed" and equanimity is shaken. If this or that work does not succeed, one thinks: "My work has failed" and equanimity is shaken. If wealth or loved ones are lost, one thinks: "What is mine has gone" and equanimity is shaken.

To establish equanimity as an unshakable state of mind, one has to give up all possessive thoughts of "mine," beginning with little things from which it is easy to detach oneself, and gradually working up to possessions and aims to which one's whole heart clings. One also has to give up the counterpart to such thoughts, all egoistic thoughts of "self," beginning with a small section of one's personality, with qualities of minor importance, with small weaknesses one clearly sees, and gradually working up to those emotions and aversions which one regards as the center of one's being. Thus detachment should be practiced.