Both Laertes and Polonius believe that Hamlet cannot be sincere in his profestation of love. Of course, they also have just come from court in which it was clear that Claudius is in control and Hamlet is a bit out of favor. But Laertes could also be trying to protect Ophelia from being hurt. He is warning her that Hamlet could be used as a political tool in an arranged marriage.
Ophelia could be played as very young and innocent, in which she accepts Laertes' advice at face value, but her next speech suggests that she realizes that Laertes is lecturing her on chastity and yet running off to France (well known for its licentiousness), so he is being a hypocrite.
These lines are often quoted as sage advice, but we must be aware of the character who is given these lines. Probably Polonius would have been played by the same actor who would have played Feste, Touchstone, the Fool in Lear. Polonius is an idiot. He is spouting hot air, advice that just sounds good. Like Horatio who as a scholar knows the reasons a ghost might return, Polonius also knows the lists of good advice for a father to give his son at parting.
One of the problems with this philosophy is that if one is a Machiavellian, one can certainly be true to himself and still untrue to everyone else. Iago is completely true to himself and yet acts falsely to Othello, Desdemona, Cassio, Roderigo, and even his own wife Emilia. Claudius is true to himself but false to Old Hamlet and Hamlet, yet he may be true to Gertrude and Polonius (except that he doesn't tell them that he murdered Old Hamlet).
Again, an innocent Ophelia may be sincerely confused here, or she could be willing to take advice from her father.
Polonius gives Ophelia the same advice that Laertes did.
Although this is hypothetically the proper reaction for a daughter to make, and certainly in Shakespear, daughters who deliberately disobeyed their fathers do not fare well by the end of the play: Desdemona and Juliet who marry without their fathers' concent are both dead by the end of the play. Katherine in Taming of the Shrew does obey her father and marry his choice; Bianca sneaks off to marry her choice (though her father had also come to an agreement with the person he thought was Lucentio) and so she is not the main heroine. So perhaps Ophelia should have disobeyed her father (arguing as did Desdemona that she should be allowed to owe duty to her love just as her mother prefered her father to her mother's father). But she does not, and eventually Hamlet turns against her because it is clear that she is willing to be a spy for her father. Ophelia ends up with nothing: no love with Hamlet, no father, no sanity, no life.