Already happening.
Your statement might as well be past-tense.
Which is why it may be time to add 'strict' to Constitutional Conservative as an identifier.
This too was predicted. The term "conservative" has been used to describe Republicans, because compared to the Marxists, they have been. It has been a relative thing only these last twenty years, not an absolute by any metric.
I have used Conservative (capitalized) to denote the difference between those of us who are for an Originalist interpretation of the Constitution vs those who are merely relatively conservative compared to the progressives, moderates, and rabid Communists on the Left.
That distinction is lost on most folks, and the term "conservative" has become polluted by the leftist convergence of the Republican and Democrat Parties in practice.
Without a modifier such as Originalist or Constitutional, the term has become meaningless.
Unfortunately, the meaning of conservative has already been fragmented with hyphenations such as paleo-,neo-,so-, etc.
Like "American", once you start hyphenating the term, it promotes division rather than unity.
We knew this was happening, the distinction between Republican and conservative has been reiterated ad nauseum, but in popular usage, the two are equated.
Either we demand Republicans not use the term unless they actually are, a stance which is unenforceable, or we find a different term to denote those of us who are morally, fiscally, and socially conservative who believe the restoration of the Republic requires a return to the Constitution as originally intended.