You can certainly convert to these groups, but there is a big cost.
There are several types of Amish. The Old Order Amish are the ones you commonly think of: buggies, etc. The Beachy Amish, however, drive cars and are a little more "out there" outside their own community. You'd stand a better chance being accepted into (and being part of) a Beachy church.
There are Mennonites (called Wenger Mennonites) who drive buggies similar to the Amish. There are Mennos on the other end of the spectrum who wear normal modern clothing, women with cut hair. They believe much more in the spirit of Menno Simons and the Anabaptist path than the letter of the law (which in most cases was man-made to begin with). You would have no problem hooking up with a Lancaster Conference Mennonite church. Beware that some are getting rather liberal, accepting homosexuality, but for the most part they are still conservative.
Very odd.
That's just great. Interbreeding on the one extreme and homosexuality on the other. Not much of a future there, genetically speaking. Seriously, I think a problem with these insular, legalistic groups is pride. That, and a stubborness to accept change even when it makes sense. I don't know what the answer is when a group is so legalistic that legalism becomes their religion. Often in Christianity when a group becomes too legalistic, there will be a schism and people will go their separate ways (even if to form new legalistic groups). How does one begin to tell a group of people who all originated from the same 1,000 ancestors 400 years ago that they literally ARE wrong?