Is the marriage of a Hanafi man to his maternal cousin valid if he touched her mother with lust, and then married the daughter according to the view of the majority who do not prohibit that by mere touching?

There is no harm in acting upon the opinion of the majority, which states that a woman is not forbidden (for marriage) by a man touching her mother with desire, and in this case, the man's marriage is valid. The mere belief in prohibition does not prevent one from retracting a previous adherence to a particular opinion (taqleed).