Voting at all, in any election, can result in appearances on mailing lists. Heck, even registering can get you mail. That said, that kind of mailer won't be candidate specific. At most it would be party specific. It looks like Kansas does require party registration to vote (although you can choose Not Affiliated), although other states may not.
I tried reading the Kansas Republican caucus rules, but it's unclear if they are secret ballot or not. Republican caucuses normally are secret ballot, but Kansas can create its own rules. It looks like the counties determine the rules with oversight from the state party organization.
The Kansas Democratic caucus is not secret ballot. Anyone attending can see for whom each person votes. This is deliberate to allow people to lobby others to support their candidates. So if you want to vote for Sanders and they support Clinton (or vice versa), they'll be able to tell.
If your family and you favor candidates from different parties, it will be possible to tell. Just participating in the caucus is public information and may generate mailers. Of course, you aren't limited to getting mailers from the party you supported, so this may not be that big a deal. For example, if it's Clinton vs. Trump in the general election, Clinton may send mail to Republican female voters who are single. And Not Affiliated voters will be mailed in the general election. Probably for both candidates.
Note that you also face the possibility of the neighbor saying something like "I thought you were all Republicans, but I saw Sidney voting in the Democratic caucus." Or vice versa.
You absolutely should not indicate that you might be willing to donate to or volunteer for any candidate. Once on those lists, you'll get mailers forever. Unless you donate enough to get mentioned on a public filing, it's not exactly public information. But it's not secret either. Campaigns turn that information into the party which will show it to other campaigns.