The Republican Party is the only realistic path to change
We live in a country that is basically split 50-50 between Republicans and Democrats. Because of that, one of the two major political parties is the only realistic option to get positive change on policy. There may be a lot of things to like about the other parties (depending on where you stand ideologically) but as it stands now the Republican and Democratic parties are the only real option to get the policies you want. You have to win elections to get the policy you want.
With that said, here is a tweet from David French:
I no longer consider myself a Republican. I’m a Christian and a conservative who evaluates each race on the merits — and I’m happy to vote third party when appropriate. The “R” by a name no longer indicates that the candidate likely shares my values or political goals.
Here is the problem with that argument: Voting for any Democrat at the Congressional level will be counterproductive, no matter how "conservative" he may be. The speakership and committee chairs matter. That is also the case at the state legislative level. We had a socially conservative Democrat representing Monroe County for 14 years, but every time she voted to select a Democrat as speaker she negated her votes on things like limiting abortion. Democratic committee chairs, speakers and Senate majority leaders have immense power in shaping the legislative agenda.
The ascension of Donald Trump has been problematic, both with some of the things he says about policy and (more importantly) the win-at-all-costs mentality that suggests even conservative principles are negotiable when it comes to "owning the libs." If we have no loyalty to our principles, it does not matter how often we "win" because the point is to get good policy.
The answer to this is not to leave the Republican Party. The answer is to work at the grassroots to move the party back to a conservative, limited government direction. Get better candidates in the primary and at state conventions. Hold elected officials accountable and challenge them in the primary if they stray too far from conservative principles. Finally, there is one critical thing to remember in the age of Donald Trump: For all of Trump's mouthing off, his policies (apart from raising import taxes) have been down-the-line conservative. French is too willing to throw out the good things we have gotten from Trump because he does not personally like the President.