There's a very far step from "Star Trek: TNG is racist and sexist." to "I find parts of this specific episode made in poor taste."
First off: I don't agree with OP. Maybe I myself am too bigoted to see it, but there's no apparent racism in that episode, at least of what I remember. At worst, the only racism I could fathom would be towards a fictional race. If it's because Michael Dorn is black, then you're seriously leaping to conclusions, considering he's playing a character who's race is aggressive by nature. One, by the way, who is by far one of the most sympathetic characters in the series, precisely because he's not one of the "evolved" selfrighteous humans; If anything, there'd be prejudice towards white people who seem to be very pretentious.
I can choose to notice the subtext and feel clever for being more socially aware than a 25 year old show, or I can take it as intended.
Second: When you're dealing with an old show, you have to remember that things were different when they made the show. I'd like to say we've progressed, but seeing the reactions in this thread and in general when it comes to sexism, racism and so on, it's very clear that we've gone from people who base their judgements on experience, to people who have an idea of what's right, but little experience to back it up and therefore act like total douchebags while calling anyone a racist, sexist or other derogatory term while having no experience with actual prejudice. Hence the amazingly selfrighteous and clueless wave of feminists(and their white knights) these days.
Sexism is prevalent through TNG and still is today in some form or another. Including sexism as a theme, does not make a show sexist. Playing on token female characters does, but there is a degree of sexism in play; While it might be mildly inappropriate it's not sending a message that women are worth less than men, unfit for command, incapable or other detrimental suggestions.
As for your subquestion, whether an animal can rape another animal:
Animals don't date out of respect for the other gender and their equal rights, but mate because of strength and other practical qualities, so there's no subtle rape like taking advantage of a drunk girl. I'm sure some animals don't consent and either try to fight it off or run away, which would indicate that it exists. In context, I think the question is pointless, since they're animals at the time and aren't burdened with the emotional ramifications or social pressure that sentient beings are.
Basically I understand that it offends you that Troi is raped, however there's no evidence of that action. I was wondering what the hell you were talking about, until I went and read the synopsis and confirmed that there was no rape, just a primal desire by Worf to get it on with Troi, but never getting to it.
Troi was raped in a different episode. It happened through telepathy and raised some interesting questions, considering that there was no physical act.
All in all, Troi is a pretty bad character, maybe because the actor couldn't live up to presenting herself as more than a bystanding commentator or the scriptwriters had no idea what to do with her. I personally think she just did a bad job overall and should've been kicked after the first season.