Would thanking the losing candidate look like changing sides?

I wrote, "Thank you for the hours you put into the campaign," and then left the message unsent.

The defeated council candidate is someone I know through the town's amateur theatre group. I supported her opponent. We disagreed about the campaign, but she still lent us scenery and turned up for rehearsals. After the result, she sent a brief message saying she'd be taking a few weeks away from group work.

A theatre friend says sending my thanks would be patronising because I helped the person who beat her. Another says I should add that I hope she stands again. I don't know whether I do.

I'd like to acknowledge her effort without offering a political compliment I don't mean or expecting her to make me feel comfortable. Is a simple private message appropriate, or would giving her the space she requested be kinder right now?