There's several versions of this, and it comes from different mindsets and different assumptions, so I don't want to tackle this as if it is all the same thing.
The first and most obvious is when non-Pagan strangers ask me if I'm a witch. There are two general versions of this; the one where the asker does not sincerely believe that I am a witch and is asking me it as a mocking question, and the one where the stranger has correlated my outfit with the idea of the fantasy sorceress and genuinely thinks that I might be a practitioner of the occult; and the rarest sort is that some have a vague idea about Wicca and modern Witchcraft and have spotted a pentacle or moon symbol somewhere upon my person, but most of those that ask are of the first two sorts, and of the second sort, they seem to think that I spend my Saturdays sacrificing goats on windswept hillsides or something with the look of fear they give me, and there's a subset of this group who are very intent on saving my soul from the Devil.
Goth is not a religion, it does not require being a member of any religion, and you get Goths of all religions (Go look at ::Priestly Goth:: and its sister site, ::Priestly Goth Blog:: - the pages of a Pastor, painter of icons, Goth and political blogger. Not the only person who has chosen a Christian religious life that I know that also has a Goth streak!) and of none. I do think that as Goth has a Romantic aspect to it, that it tends to attract people who have a spiritual nature about them, and while yes, there are higher percentage of Goths who are on mystical and occult paths than in the general population (and I include in that Goths who follow the more mystic aspects of mainstream religions, too), it is by no means that all Goths are Pagans.
I always find it hard to deal with these situations; I usually start with "that's an unusual question" - after all, how many other people has this person asked this question to? Probably not many, if any - and then try and figure things out from there. I don't use the word "witch" very much anyway, as I have explained in ::this:: earlier post, but my answer is going to be very different between someone who says "I noticed your pentacle ring and thought you might be Wiccan" and someone who says "Don't you Gothics (An aside: Gothic is an adjective, not a noun! People need to learn this!) worship the Devil?" I never lie, but I tend to word things carefully to neither confirm nor deny and to steer things away from me, personally. If people are ignorant but genuine curious, then I try to politely explain that they've been misinformed, if they're judgemental and going on a religious tirade, then I extricate myself from the situation. Whatever I do, I'm conscious that it will reflect on Goths as a whole, and therefore try and be as polite (but sometimes firm) as possible and make sure I do not let things devolve into an argument.
Those who think I am some kind of crazy person and that my clothes and religion are both signs of this probably are not going to listen to any protestations otherwise, so I feel the only answer is to be a calm person and let my actions, and for those who are more than just a judgemental stranger, my life demonstrate that I am not some person wildly disconnected from reality and trying to live some delusion that they are in fact Morgan La Fey or something (there's nothing wrong with the occasional bit of dressing up as long as you're fully aware it is only a costume.) and that I am no crazier or more deluded than any other religious person may be, as there will always be the more militant atheists who try and make an issue of any religion, especially fringe religions. I am of the opinion that as long as a person is not hurting others or themselves through their religious choice, it is of no concern to others and that if you wish to engage in religious debate, it ought to be a polite discourse and not a personal attack.
Prejudgement from Other Pagans
I am certainly not into Neo-Paganism as a way to deeper entrench myself in the 'spooky woman' role; this is not some blurring of the lines between everyday life and L.A.R.P. I was pagan before I was Goth, by about three years, although I definitely had Pagan attitudes and ideas that aligned with Neo-Paganism long before that, right from when I was a small child, although I did not know what Neo-Paganism was then.
To be fair, the Neo-Pagans I am currently involved with in my local area seemed pretty open and willing to give me a chance when I joined groups and starting getting involved with the Neo-Pagan community here, and I think that's partly because as the Alternative community in general is small here, people who stand out because they act and dress differently and their thoughts do not align with those of the majority, stick together, whether they're hippies, Neo-Pagans and Witches and other people who practice Alternative spiritualities, Metalheads, Goths, or any combination of the above or people who I haven't mentioned yet. My encounters with Neo-Pagans who have been judgemental have primarily been online. I think the internet is a medium through which some people forget their manners, as there is a distance in typing at a screen that can make people fail to realise there is still another human somewhere reading a different screen at a different keyboard, but not that unlike them.
The other assumption about being a Goth and a Neo-Pagan is that there are other Neo-Pagans who think that we practice curses and magic for evil purposes, that we sacrifice living things and are liable to commit some kind of sacrilegious practice or whatnot, and I think that comes from the same misinformed place as the non-Pagans that think this; they think Goth is somehow linked to 'black magic' (side note: magic does not come in 'black' and 'white'; a growth spell or a love spell can be just as destructive as a diminishment spell or separation spell, and the latter two can actually be used helpfully) and evil practices, and it just is not! It is a common misconception, but it just is not true. Goth does not have any religious affiliation, and does not involve a deliberate desire to be purposefully immoral in any spiritual or more mundane way.
As per usual, I remind people to check their assumptions, or rather, to try and avoid assumptions and to approach things from a place of learning. Goth is a subculture encompassing fashion, art, music and an appreciation for darker things; it is not an anti-moral code, a religion or a cult and has no bearing on what a person choses to be their religious, spiritual or atheist path.