I think that perhaps the "Ladies of the day" such as Holly Woodlawn, author of "A Low Life In High Heels" and others may differ with you somewhat. That time (late 60's) was rather dynamic socially on many levels. The Drag Queens and other transgendered persons remained transgendered even as acceptance grew.
I can accept that there may have been some who chose to dress feminine at the time, as some may even today, but I don't believe that cross-dressing to "fit in" has ever been a large part of either the Transgendered or Gay communities. Acceptance of someone who was less than sincere about their identity, either their gender identity or sexuality, would have been far more difficult in those troubled times than it would be even today.
