Speaking as an actual college professor (albeit one in a hard-science field where political issues literally never come up in connection with the vast majority of the course material, and who also maintains a personal rule against using office space or regular institutional duties as a free bulletin board for advertising general political opinions), I’d offer the following advice:
1) As other posters have noted, figure out what you really mean by “targeting”. A professor merely disagreeing with or criticizing your opinions is not the same thing as a professor actually being unfair to you because of your opinions unrelated to your abilities or performance in the course.
2) Study your college’s student code of conduct, mission statement, harassment/discrimination policies, and other information that spells out what behavior the institution officially considers ethically unacceptable. A surprisingly large number of conservative students come in with a chip on their shoulder about their rights to “freedom of speech” and “academic freedom” and what not, while apparently never noticing that they have contractually agreed to abide by the institution’s rules limiting their freedom to express certain kinds of opinions.
If your college has a policy statement along the lines of “committed to creating a welcoming environment for the campus community without bias on grounds of race, color, sex, pregnancy, religion, creed, national origin (including ancestry), citizenship status, physical or mental disability (including AIDS), age, marital status, sexual orientation, gender identity and expression, military status, predisposing genetic characteristics, domestic violence victim status, or any other protected category under applicable local, state, or federal law”, etc. etc., and you open your yap in class to say it’s unnatural and unwholesome for gay people to want to get married or for people to identify as transgender, you may be violating those anti-bias principles. A professor who shuts down your anti-gay or anti-trans or similar remarks, or points out that they’re bigoted against gay or trans people, is not “targeting” you: they’re doing their job in supporting the official policy of the institution.
If you feel that that’s an intolerable limitation of your freedom of expression, then as other posters have said, you need to seek out a different institution with different official policies. Don’t expect the college, whose rules you agreed to abide by when you accepted their offer of admission, to start bending or ignoring those rules just so you can express what you consider to be your fundamental conservative beliefs.
3) If, on careful consideration of points (1) and (2), you still feel that your professor is really out of line in gratuitously picking on your legitimate conservative opinions, then take detailed notes of at least two or three incidents that clearly illustrate that (which is good for your note-taking skills too), and approach the professor about it in a courteous and open way. Explain that you feel unfairly singled out for reasons that aren’t related to the course material or your performance in the course, and listen to what they have to say about their interactions with you.
4) If the professor really won’t listen to reason in response to your good-faith attempt to discuss the situation, make detailed notes of that exchange as well, and talk to the department chair and/or a dean about your concerns.
5) In the case of interactions with other students, review points (1) and (2). If you still feel you’re genuinely on the receiving end of unjust and unwarranted illtreatment, make some more detailed notes about the incidents that concern you (your note-taking skills are going to get so good! :)), and talk to your Residential Advisor and/or a dean about them.