I do not completely agree with Alexander Eremenko's answer (though I understand his point - just hope the following does not sound too provocative).
Was Italian algebraic geometry at the beginning of the XXth century providing proofs of their statement? Yes, certainly, though a number of them turned out to be wrong, therefore not rigorous. And yet their arguments revealed a good amount of informations on "true" algebraic varieties once some additional hypothesis were added. Certainly at the time there were published there was wide consensus on the fact that those proofs were rigorous.
Were papers published in many URSS journals between the 50ies and 80'ies rigorous? Proofs usually were given in the form of very brief hints on the line of thought of the proof and details were abundantly left to the reader. Still there was a widespread consensus on the fact that those can be considered proofs, sketchy as they were (and some of them turned out to be not completely correct after all). Would they have been accepted in a Western math journal without questioning their correctness at the time? Probably not, so that one should say that the standard of rigor was at least country-dependent.
A proof is a couple of different things. A completely clear and rigorous set of steps from some hypothesis (and under some agreed upon set of rules which, as Kopylov remarked, were never completely agreed upon, see the dispute around Axiom of Choice). But in this sense proofs exists only in dreams - or rather, at present, in computer-verified proofs. Then, also, they are a way to communicate to other mathematicians a line of thought, more or less detailed, around which a community agrees that it can be turned into a rigorous and complete proof. And here you see my choice of words: "communicate", "community", "agreement" - it is partly a social issue and as such it changes with time and place.
Is a "proof" what it is supposed to be if there is no one on Earth able to comprehend it? Not so sure about it. Mochizuki's proof of the "ABC" conjecture comes to mind here. But what about the classification of finite simple groups? Are we sure it is proved if after its "proof" so many different mistakes were found and fixed, or do we simply just believe in it?
Is the authority of who states the proof really, in practice, not relevant? Are we really ready to accept that an argument is a proof if it comes from an unknown amateur researcher with no affiliation and no previous research record than we are ready to accept it from a Fields medalist? And how it comes so, if proofs are carved in marble for eternity?
How it comes that we feel safer about a statement in math if we know that it can be proved with different techniques? A statement is true or false, after all: but in our research experience we remember way too well of that many times that we strongly believed that some math statement was true (as a consequence of very convincing arguments) and later realized it was wrong.
So my answer to this question is: a math proof is always, partly, a "social contract" and from this perspective no doubts that its standards changed and will keep on changing.