To answer the title in a word, no. But don't go letting your head explode on me just yet. Keep reading please because I have two things to say to qualify that answer.
1. Nowhere in scripture are we called to "love the homosexual". What we are called to do is to love our fellow sinners. To say that we are called to love the homosexual does two things. First, it gives a particular sin a feeling of specialness. The special attention this sin receives is the result of bleed-over from our culture into Christianity. Second, it allows the sinner to adopt his sin as an identity. What man, given the definition of adultery that Jesus gave, is not an adulterer? I'd say the vast majority are, given the low bar set by Jesus for becoming one. But I've yet to see anyone proclaiming, or demanding, that Christians ought to love the adulterer and stop judging him and to be more accepting of his special sin.
2. The second is more important. The command in scripture to "love" our fellow man, that is those who persecute us, those who are enemies of God, and a host of other sinners, ought to have us examining the verb "love". Scripture is not silent on this matter, but let me first say that nowhere does scripture confuse the word love with acceptance. The common mantra of our day is that Jesus accepts the sinner wherever he is. I don't think that's true. Jesus loves the sinner wherever he is, but he rejects his sin. For example, let's look at an occasion that does not carry the cultural baggage of the modernday homosexual; the rich young ruler. Jesus did not accept this young man's sin of idolatry, yet the scriptures tell us "...Jesus felt a love for him... ". (Mk 10:21)
The modern Church is constantly admonishing us to love like Jesus loved. But I can't help but to think that there is a difference between what we're being admonished to do and what scripture teaches us to do. From the beginning to the end of Jesus' ministry his sermons can be summed up by "repent for the Kingdom of God is near". He did not preach "accept sins that are popular in your day".
To be sure there is a caricature of Christians who are pointing their fingers in angry self-righteous indignation and demanding repentance. While I'm sure there are some who do this--and we are supposed to love them too by the way--this does not mean that we are to be more accepting of a popular sin in order to mitigate that caricature. That would be folly.
In short, we are not to confuse love with acceptance. While it is certainly possible to love without accepting there is a very real danger in our present age of unwittingly not loving while accepting.
So, are we to love the homosexual? No, we are to love the sinner, every sinner, enough to call him to repentance in a compassionate and loving way.
Ephesians 5 Marriage and Divorce - Okay, so it's somewhat of a large passage. But it's necessary, so I'll put it down here and then refer to it as we go: 17 Therefore do not be foolish, but ...