I'm curious about where Felicifians stand on the free will-determinism axis. And should it matter to a utilitarian?

There was a thread on your first question not too long ago, although I can't find it now.
The second question (should it matter...?) is one I spend a lot of time thinking about. I'd say it doesn't matter as far as judging the morality of actions (or rules) is concerned but does as far as judging the character of actors. The former is the focus of utilitarianism. So I believe the short answer to your question is no. For a variety of reasons, I think free will is either non-existent or weak (haven't fully decided) and judging people's character is therefore misguided (although we all do this anyway).

OK, here is the thread: http://felicifia.org/viewtopic.php?f=10&t=651&hilit=determinism
I think this thread (unlike the previous one) raises the important question of what relevance the topic has to utilitarianism. So I hope people will post in this thread.

I'd give fairly high credence to the view that everything that happens is a consequences of previously existing conditions together with physical laws, which are either deterministic or stochastic in character. And I think that this is not consistent with the existence of moral responsibility. But I don't think that this is all that important from the point of view of a utilitarian.

Some time ago I believed that free will couldn't exist because it was logically inconsistent. After thinking it true I recognized that I even didn't know what free will had to mean. I simply couldn't imagine anything that was neither caused by chance nor by determination (reasons are a form of determinations, too I think) but by something called "free will".

As long as free will does not alter our subjective probability of a person if we try to influence him/her doing the good it does not matter, if only the expected consequences are counting.

I think determinism is probably true. Besides just randomness, I don't know what 'free will' could mean or why it implies personal responsibility. To some degree or another, I'm permanently agnostic about everything outside of my own conscious experience (including what causes conscious experience).

And should it matter to a utilitarian?

I don't think it should. Even if people are responsible for their behavior, causing murderers, rapists, bullies etc. pain (and taking pleasure in or being consciously indifferent to their pain) is still evil.

judging people's character is therefore misguided

I still think that some character traits should be acknowledged as morally desirable (like compassion/empathy) and undesirable (like egocentrism, sadism/ cruelty/ schadenfreude ). Even if no one can be blamed for being cruel or sadistic, these traits should still be discouraged.

I've heard it suggested that the idea of free will is caused by the fact that they way we make choices involves considering alternatives, giving the impression of alternatives.

For example, if you have a simple chess-playing program, it will look at the board position based on its actions and its opponents actions. The program is deterministic so there's only one thing that the chess program can really do, but it still has to consider alternatives. If it doesn't, it won't work.

I'm not entirely sure what it would mean to say the feeling caused by that is accurate or inaccurate.

As for determinism, I think the universe is deterministic. The only nondeterministic interpretations of the laws of physics seem deeply flawed for other reasons. I don't disagree with the idea of stochastic laws on principle. There's no reason the laws themselves had to be what they are, and thus there existence is essentially stochastic in the first place.