I never had the sense cloppers caused excessive friction within the community---at least overtly. As is in keeping with the Zeitgeist of the 21st century, bronies tend to display a "live and let live" attitude toward cloppers, so long as they don't impose to their habits on others. Clopping is nevertheless a more sensational aspect of the brony phenomenon, if only due to the fact the main characters are equines. But the sexual fascination found among a segment of bronies is not idiosyncratic; most every fandom crafts out its own little niche where such activity is visible. Nobody is going to go after, say, some Sonic fans who fantasize about the characters, because that ground has been covered and it does not garner a lot of attention. Given that bronies are receiving press coverage and focus from media sources, people are going to more readily dig into the arguably unsavory facets of the fandom.
Again, clopping only seems to be an issue when it is made an issue. Otherwise, how often does it otherwise come up when the show is being discussed? Most of the focus of outsiders falls upon the fact a number of adult men are heavily invested in a cartoon show aimed at girls. In that respect, bronies more readily rally against attempts to pigeonhole the entire community as weird, socially backward, and disturbed. Because clopping feeds into that stereotype, it quickly raises everypony's blood. That is how I view it, at least.
I cannot readily think of a major conflict within the community. To me, arguments over shipping and clopping quickly become proxies for other issues, i.e., those concerning general sexual morality. Other arguments tend to be rather fleeting, e.g., disagreements over character interpretation. Our biggest conflicts tend to be external, usually involving the perception of the fandom and the occasional accusation (which may or may not be true, depending on the circumstances) that bronies force MLP onto others when they wish to be left alone. The worst problem bronies face is probably bullying by those who do not understand, refuse to understand, or simply desire to engage in tearing down others.