What reasons do Laertes and Polonius give for their command to Ophelia to stop seeing Hamlet? Are they reasonable?
Laertes tells Ophelia that she should think of Hamlet's feelings as something more akin to lust or infatuation rather than love. He says that she should consider them as "The perfume and suppliance of a minute / No more" (1.3.10-11). However, even if Hamlet does truly love her, Laertes believes that he will not be able to choose his spouse for himself due to his royal status. He says,
"He may not, as unvalued persons do, / Carve for himself, for on his choice depends / The safety and the health of this whole state" (1.3.22-24).
Further, he calls Hamlet's potential sexual desire a "danger" to her and constructs a rather graphic metaphor about a cankerworm that destroys the young flower buds in the spring to show how a sexual relationship with Hamlet will ruin her. He does seem to give Hamlet the benefit of the doubt, believing that Hamlet honestly does have or thinks he has genuine feelings for Ophelia.
When Ophelia speaks with her father, Polonius, he advises her to make herself a little more scarce when it comes to Hamlet. He tells her,
"Do not believe his vows, for they are brokers, / Not of that dye which their investments show, / But mere implorators of unholy suits, / Breathing like sanctified and pious bawds / The better to beguile" (1.3.136-140).
In other words, she should not believe Hamlet's pretty words of love because they are really meant to deceive her and lead her into a sexual relationship. He is ultimately suspicious of Hamlet's motives and the danger they pose to his daughter's reputation.
Given the time period, these do seem to be reasonable concerns. If Ophelia engages in a sexual relationship with Hamlet, her reputation could be ruined absolutely, and it seems understandable that her brother and father would be concerned for her, especially because they would be tainted by her disgrace.
Laertes suggests Hamlet's attentions were essentially youthful passions driven by a young man's hormones, and that they'll pass.
He also suggests that the difference in their status (royal vs. non-royal) leaves Ophelia at much greater risk: she could lose her virginity and her heart, and Hamlet nothing, due to the differences in power and rights.
Polonius makes similar suggestions, saying that he knows from his own experience what men will say when the passion drives them (suggesting that they lie, and/or promise more than they can deliver).
Are they reasonable? Well, knowing guys, yes, the concerns about hormones are reasonable. The concerns about power are too. However, both treat categories, not Hamlet as an individual, and so are somewhat inaccurate.