The Ashkenazi nusach of V'lamalshinim omits explicit mention of heretics. Therefore, recitation or omission of this blessing by the prayer leader seems to no longer serve as a signal for whether he is a heretic (or does it? If so, please explain).
Further, it seems likely that a large class of modern heretics would even be willing to recite variants of the blessing that explicitly refer to heretics.
(Note: Answers that can sufficiently rebut any assumptions made in this post are welcome).
The Talmud (B'rachos 29a) teaches:
Rav Y'huda said in the name of Rav: If [a prayer leader] erred in any of the blessings [of the amida], we do not remove him. [The exception to this is] if he erred in the blessing of the Sadducees (alternatively, the blessing of the heretics). We remove him because we suspect he may be a heretic.
The Shulchan Aruch (OC 126:1) codifies as halacha that we remove a prayer leader who entirely omitted the blessing of V'lamalshinim. The L'vush (126) explains that we are concerned that the reason he omitted V'lamalshinim is that he is actually a heretic and "he does not want to curse himself." This is based on the commentary of Talmidei Rabbeinu Yonah on the Rif (B'rachos 19b in dapei haRif):
טעה בברכת המינין מעלין אותו דחיישי' שמא מין הוא ומה שלא אמרו שאם טעה ולא הזכיר תחיית המתים שמעלין אותו ג"כ מפני שברכת המינין יש בה קללה למינין וכשאינו אומר אותה אנו חוששין שמפני שהוא מין אינו רוצה לקלל את עצמו אבל בברכת תחיית המתים כיון שאין בה קללה אין בזה היכר אם הוא מין או לא שאפשר שאפי' שלא יאמין הוא בתחיית המתים עכ"ז יאמר הברכה דמאי איכפת ליה אם יאמר מחיה המתים כיון שאינו מקלל עצמו הלכך כיון שאיפשר שיאמר אותה ויהיה מין ולא נוכל להכיר אותו אפי' כשלא אמר אותה אין מעלין אותו
עוד נוכל לומר שבתחיית המתים כשטעה אין מעלין אותו מפני שאפשר שהוא מין ומאמין בתחיית המתים
The above commentary suggests that a heretic does not want to curse himself, but he is willing to recite other blessings that are at odds with his beliefs.
According to nusach Ashkenaz, which doesn't mention heretics explicitly in the blessing, why would a heretic avoid reciting this blessing?
Even the other variants of the prayer that mention minim (heretics) do not specify particular beliefs or groups (e.g. Sadducees, Boethusians, or Therapeutae). A particular heretic might therefore not read V'lamalshinim as being applicable to him; he might not consider himself a heretic. Why, then, would he balk at using the generic term for heretic in the prayer? Is it possible that the term "minim" was so well understood to mean sects other than the P'rushim (Pharisees) that even a Sadducee would consider himself a min?
Conversely, if a heretic would not avoid reciting this blessing, why would we rule that a prayer leader must be removed for omitting it?
In light of Josh Waxman's answer, I would like to clarify what I meant by my first and third questions above; they are not questions on the gemara, but rather questions regarding the halacha as it pertains to the modern Ashkenazi variant of the prayer that excludes mention of heretics. Background to those questions follows:
Ashkenazi poskim such as the Mishna B'rura (126:4) seem to apply this halacha of removing a sh'liach tzibbur even in light of the current predominant Ashkenazi nusach that does not explicitly mention heretics.
Some poskim, such as the K'nesses HaG'dola (126), have decried the practice of omitting mention of heretics, and the Mishpat Tzedek (Vol. 2, §9; early 17th century) discusses whether a chazzan should be removed for mentioning only lamalshinim and not lam'shumadim. The Magein Avraham (126:1) is likewise unsure whether a prayer leader must be removed if he mentions malshinim but excludes mention of heretics, though the Magein Avraham mentions that the nusach of Romania includes only v'lamalshinim.
The Magein Giborim (126:1) expresses surprise that the Magein Avraham didn't mention that this is our nusach, too. The Magein Giborim seems to conclude (if I'm understanding it right) that it is forbidden to deviate from our nusach of v'lamalshinim:
ומהתימא שלא כתב שמנהגנו הוא לומר ולמלשינים כבני רומניא ועכ"פ לשנות הנוסח' בברכה זו ודאי אסור
The Aderet, however, comments that this is a mistaken nusach, and advises that people switch back to another version in their silent amida that includes reference to either lam'shumadim or lakofrim (T'fillas David §13, cited here). Even the Aderet, though, says that a prayer leader should adhere to the accepted nusach in public to avoid leading to a radical fragmentation in community practice based on what each individual thinks is appropriate ("שלא לתת שתהיה תורה ביד כל אחד").
The Mishna B'rura (ibid.) says that a prayer leader is not removed for using the nusach of v'lamalshinim that excludes mention of heretics, because there are places where this is an established nusach.
In any case, by the standard described in the above commentary of the Talmidei Rabbeinu Yonah, who reject the notion quoted by the Tur (126) in the name of the Y'rushalmi (B'rachos 5:3, "לכל אין מחזירין אותו חוץ ממי שלא אמר מחיה המתים ומכניע זדים ובונה ירושלים אני אומר מין הוא") that someone omitting תחיית המתים should also be removed, it would seem that modern Ashkenazim should no longer remove prayer leaders who skip the entire blessing of V'lamalshinim. This is because its recitation would not indicate that the prayer leader is a believer (per the rationale of "אין בזה היכר אם הוא מין או לא" that the Talmidei Rabbeinu Yonah commentary gives to explain the implicit ruling in the Bavli that omission of the T'chiyas HaMeisim blessing would not be cause to remove a prayer leader).
Additionally, per Dave's answer and Shmuel Brin's comment, it's possible that this problem would apply nowadays even to nuscha'os that explicitly mention heretics (unless offense rather than fear would still motivate modern heretics to omit this blessing).
So why is the halacha to remove a prayer leader who omits the blessing of V'lamalshinim still applicable?