If you need science to be a good person you're probably just as morally rotten and corrupt as someone who must have a Bible to instruct them to engage in pro-social behaviors.
Philosophy has been exploring and solving these things for thousands of years. After all, science is utterly unable to give us ethics. It can't. At most it gives us some more pieces of the puzzle.
Science provides you with pretty vital information which in turn allows you to make ethical decisions.
The better informed you are about what well-being is about, what suffering is about, what the consequences of your actions are, etc... the better equipped you are to make informed ethical decisions.
I'ld say that the "ethical" part of your choices have to do with your motivation.
I'ld say the result thereof, the success you'll have, will come from your understanding of reality in all aspects relevant to ethical decision making (which is to say: how your decisions affect well-being / suffering).
For example...............
If your "understanding" of the world is that being gay is a "lifestyle choice" informed by the devil and "against god", then you will with the best intentions think that being homophobic and having anti-gay legislation is an ethical way to go about it.
If however, with the help of science, you understand how being gay is a matter of biology and aren't bound to certain dogmatic iron age myths, and how as a gay person being confronted with anti-gay situations in all forms is detrimental for psychological (and sometimes physical) well-being, then you will understand how being homophobic and having anti-gay legislation is in fact extremely unethical.
In both cases you may be acting with the best intentions.
But only in the latter case will your best intention actually have a positive effect on well-being and thus an actual ethical outcome.
So I would say that there definitely ARE right and wrong answers to ethical questions. And that these definitely can be, and are, informed by an understanding of reality. And where does such understanding come from?