On a shidduch with someone not committed to Torah observance, the Rebbe's guidance is firm:
A Jewish home must be built by two people who are both committed to Torah and mitzvos in practice. Promises of future observance are not enough; look for a match with someone already living by Torah and mitzvos (IK 6778, 7122, 9489). Check not only outward compatibility but sincere religious commitment and a practical willingness to keep Torah (IK 6333).
Marriage should not be relied on to change the other person. Trying to change someone's beliefs or way of life through marriage is uncertain; real commitment has to come from within. If change is going to happen, wait until it genuinely has (IK 6750, 7122, 7269). If a prospective chosson refuses even a private commitment to live by the Torah, proceed with great caution (IK 4936).
For parents whose child is in a relationship with someone not Jewish: act promptly but discreetly. Involve the community's help, quietly create opportunities for the child to meet suitable Jewish partners, look discreetly into any claimed conversion, keep the home's spiritual safeguards in place, and avoid direct confrontation that could push the child away (IK 1771, 6197).