Is it acceptable that a Jewish man or woman become religiously observant because of their desire to marry someone they know that is already observant? Is there any problem with the possibility that they might not be sincere?
Since the person is Jewish, he or she is obligated to be observant in any case. Of course, the more sincere a person’s motivations are the better. But even if he or she is only interested or practicing in order to gain or maintain a relationship with one who is already observant, this is tolerable.
This is not so different from the fact that many observant people are committed for any number of reasons, which, in addition to the altruistic ones, might include social acceptance, recognition, honor, livelihood, etc. While these motives are certainly not ideal, realistically they exist, and if in the end of the day they contribute to a person’s observance, they have value as such.
In fact, the Sages taught that even if a person realizes his motivations are not ideal, he should not desist from observance. Rather, through lower-level intentions one will eventually grow toward the ideal. In a case you describe where the motive is for another person, the observant person, if interested, should try his or her best to guide the other toward genuine belief and observance.
This is probably the more problematic issue with the question you raise. Because even if the interested person eventually retracts from observance, G-d will not be “harmed”, and the person can always come back to G-d even if it takes an entire lifetime. But if he or she retracts after committing to another person, particularly in marriage, that can have devastating ramifications. So it’s really the observant person who has to be most careful.
The famous Rabbi Akiva was initially an illiterate hired hand of a wealthy estate owner whose daughter Rachel saw that Akiva had what it takes to become a great Torah scholar. She proposed to him saying, “If I marry you, will you study Torah?” Apparently, he was not so sure of himself, or sure of the sincerity of his motives, because the Midrash teaches us that Rachel took him on a walk with the intention of inspiring him.
When they arrived at the base of a waterfall, she asked him, “What do you see?” He replied, “Water pouring onto the rocks beneath the fall.” “Look closer”, said she. “I see the rushing water has bored a hole through the rock.” Rachel then said these piercing words: “Take heed. If something as soft as water can bore a hole through something as hard as rock, surely something as strong as Torah can bore a hole through something as soft as your heart of flesh.”
Akiva was inspired. They were married. After 24 years of extreme sacrifice and dedication on the parts of both Rachel and Akiva, he became a rabbi to 24,000 students. And it was through Rabbi Akiva that much of the Torah was preserved through the destruction of the Templeto the generations that followed.