Okiale:
There is a dispensation in halacha, (restrictions do apply, for rules and regulations please consult with an Halachic authority…) called ‘kavod habriyos’. I.e. when the honor or pride of a person will be compromised as a result of keeping a specific halachic requirement, Chazal dispensated with that particular requirement as to save that persons honor. A prime example is Tallis. It is generally prohibited (bittul aseh) to wear a garment of four corners which does not have Tzitzis attached. However if ones tzitzis tore off when he is in a public area, and taking off his attire will be a great embarrassment for him, the law of ‘kovod habriyos’ does apply, and he need not strip of the four cornered garment until he reaches a private location.
I would venture that, all the more so, where refraining from doing the mitzva will be the source of embarrassment, that this should override your minhag. This, of course, would not replace your minhag, and would only apply where you are in a place where everyone else is doing the mitzva.
(Parenthetically, I might add that a ‘scarf tallis’ or ‘neck tallis’ is not an issue at all’ because these are not considered ‘wearing’ in halacha.)
Having said that, I would like to suggest that a minhag of a conservative kehilla does not have the halachic binding of a minhag. A minhag is considered sacred in halacha for the reason that, whoever instituted the minhag, understood all of the talmudic background sources, and after careful deliberation the concencus was to act in that manner. The conservative ‘minhagim’ were enacted without that careful and honest deliberation, and therefore must give right of way to normative halacha.
Another disclaimer: Let not this be a harbinger of other modifications you would make in your observance in order to conform with your new kehilla. The conservative are not doing a great job of bearing the torch of Torah, as has been passed on, unchanging, for 3,328 years (minus four weeks and four days).