I think you are talking about problems of very different levels:
how to make those hard headed ones that don't like to use brackets in if statements,
That is mostly a style/readability issue, unless there is an explicit operator precedence problem. The latter should not be very common, and is unit testable anyway, thus easy to fix. The former can easily regress into a Holy War with little to gain, but severe negative consequences to team morale. So beware - only push tried and tested rules, which have been accepted by at least some teams/communities and proven to work.
or use the same connections string everywhere in the code,
If you mean Magic Constants, that is indeed a maintenance (plus potentially security) problem, and as such IMHO any seasoned developer will understand and accept that it is a Bad Thing.
or whatever, to use the coding rules without making them oppose the idea?
You can't force people to agree with whatever coding rules - your only chance is to get to a common understanding and buy-in from team members via discussion and (sometimes fierce) debate. You need to use logical and convincing arguments, showing the value behind each rule, and explaining how following it is going to pay for the inconvenience of adjusting ingrained habits. On the other hand, strive to make the transition as easy as possible, by e.g. introducing automated code formatting at check-in, according to the accepted rules.
Still, at times you just need to accept that people have differing opinions, thus the coding rules everyone can accept will be lenient in certain respects. Accept that and focus on areas where you can improve things with less effort.