The thing for me is to consider how likely it is you can still get the old-fashioned style in the 1860's. Is a hatmaker going to still make something that's been out of fashion for three decades, or is he only going to make and stock things from the last 5-10 years? Or could the item really last for 3 decades?It is my impression that the Victorian era was one that valued conformity and group standards far more than do we today. As fashions move on, there may be some lag to adopt some semblance of them (say, 5 years or so?), but eventually, a person has to move forward in fashion.
Men's things seem to evolve more slowly; the major changes would include trouser styles (front fall to fly construction), coats (variations in cut), hats, and facial hair. Of course, with facial hair, (and with women's hairstyles) the person's own sense of "what looks good on me" is going to factor in a LOT... hence, the picture of Clara Barton with "old" hair. Notice, though, her "old" hair still conforms to the prevailing norm of the day: center part, smooth top, fullness to the sides and back. So, she's not too Odd by fashion standards, just not a fashion plate. Which is fine.
With women's things, the styles available to most would reach back to the 50's, or 40's at the most. The 50's and 60's have a very similar bodice silhouette, with different sleeves. Get back further than that, and it's a different corset shape, different bodice styling, very different sleeves. And all of these things are easily updated over the course of a decade, even by a backwardly looking lady. If she sews for herself, she's going to be influenced by the "groups standard" in her community, so if she's still sticking to 1830's styles in the 1860's, she's going to be seen as (at best) eccentric, and at worst completely nuts, and suspect morally because of it.
If someone else sews her clothing, let's take a look at who that is likely to be: a daughter (who is more up on current fashions than she, and who might subtly update things, or just refuse to make "odd" things for Mom); a local seamstress, who may very well refuse to make completely outmoded things, for fear of her reputation as a dressmaker; another family friend or member, of varying levels of skill, who may find it easier to copy modern silhouettes, rather than have to recall or learn the old modes.
While not everyone should be "band boxed" for the 1860's, the pre-60's elements should be carefully chosen... the bonnet re-trimmed, collars newly made, dress trims replaced, sleeves updated, newer hats purchased (even if purchased with dismay that those good old styles are no longer valued by the hedonistic modern age), etc.
It's a question everyone must answer for themselves, based upon their own impression. For myself, I'm nearing 30, and have two children... the earliest I go back to for clothing is about 1855, the styles I had made just before I was married. These aren't "top fashion" items, either. But, I can update my bonnet cheaply, and since the dress styles have only changed sleeve-wise, it's not hard to copy a nice new sleeve for my newer dresses. After all, ingenuity doesn't cost my husband a penny! My ability to "keep pace" with some of the current fashions just shows that I can manage a home and my husband's income, and make the most of it.
Short answer: yes, some older modes are to be considered. But, just because something happened pre-61, doesn't mean it's de facto appropriate for the impression. Fun to ponder, though! 
Regards,
Elizabeth Clark
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